Compare these two neighborhoods for a first timer?

Both are centrally located. But two things to notice: the first one mentions that some people may be sensitive to noise, so it could be above a cafe or restaurant with outdoor dining. It is on the French first floor or second floor in the US. The second one doesn't mention air conditioning. You didn't say how many people or what month.
You can check out the exact situations by asking for the addresses and using Google to see what is below you or if buses are stopping under your front windows.

IDK your budget but our group has reserved this property in the Marais via vrbo:
Courtyard Maison Marais #1467040a

sorry- left off that info - 4 of us, last two weeks in september- so no AC shouldn't be a deal breaker. I did look around on google maps, but I guess I wanted to get a feel of what the areas (within 1/2 mile or so) are actually like? Is one livelier? more options to eat? more touristsy? more of an area were people actually live vs visit, etc?

thanks!

Based solely on location, I’d lean towards the first selection. We did some wandering around here after visiting St. Sulspice and I recall the neighborhood feeling a bit quiet and upscale. Plenty of nice cafes and restaurants. We enjoyed some time here.

I stayed in the other area twice actually. This is on a busy street and is a little more “urban Paris.” It’s actually more quiet and enjoyable in the evening, noisier in the day. You’re near two good metro lines, which is a big plus. If this place were one block off Sebastopol (sic) I’d feel better about it.

There will be plenty of cafes, restaurants, nightlife, etc near either (this is Paris after all.) But at the risk of generalizing, I think it’s kind of “genteel Paris” versus “workaday Paris.”

Personally I like the first location better. Either location is first to transport, cafes etc.... Also it's a real two bedroom vs a sleeper sofa (I have honestly never found those to be at all comfortable :) ) The sleeping arrangements look better for a large group imho.

The second is close to the Chalet metro stop which means it has great transport but... it's HUGE and confusing IMHO. And honestly I feel like that area is more overrun with tourists than the much maligned Rue Cler area.

I did rent from Vacation in Paris in March and the meet and greet was OUTSTANDING. I've rented from them before on self-check in and it can be confusing. The guy who did the meet and greet was wonderful. Took lots of time to show us how everything work and when he was checking before we arrived he noticed a broken door handle, he was back the next day with the appropriate tools to fix it (He had tools on day one but it was an old handle and needed some strange screwdriver... guess that's a risk of old buildings!)

I am incredibly impressed you actually were able to navigate the second website. Just for fun I tried to see what was available for an upcoming visit. Really buggy site :)

You are wondering about the neighborhoods (arrondissements) of Paris that the flats are located in, not the flats so much--correct? You might do a search of each arrondissement--looks like the 6th (St. Germain) and the 2nd? "Montorgeuil Area" is what is stated in the ad (unsure what exactly they mean by "area" but rue Montorgeuil is quite nice. (Correct me if I am wrong those of you who know much better than I.)
I've stayed in both and both were lovely areas. Yes, there are many places for that evening glass of wine, wandering beautiful, quaint streets, seeing well-known sights, eating, etc. I like to follow Paris Perfect https://www.parisperfect.com/st-germain-des-pres-6th-arrondissement.php and https://www.parisperfect.com/blog/2017/04/shops-on-rue-montorgeuil/. Check out Le Compas for a large terrace to enjoy that glass of wine.
Depending on when in September you are in Paris, the second apartment could be warm since it is on the 4th floor (5th floor American) if there is no AC. We will arrive September 5th, and I've made certain our apartment rental has AC. Enjoy your explorations! I find doing the research before to be one of my travel highlights.

In some years it gets up into the 80s (F) in Paris during the second half of September, so I'd be concerned about a non-air-conditioned apartment, especially on an upper floor. You can take a look at actual, historical, day-by-day weather statistics on the website timeanddate.com.

Paris weather September 2018

Paris weather September 2019

Paris weather September 2020

Paris weather September 2021

Paris weather September 2022

You can get everything you mention in both neighborhoods. I'm a Right Bank fan so I would pick the second based on location. But neither location is a dud. I do think the location of Vacation in Paris apartment is what many Americans have in mind when they think of an apartment in Paris. Based on my reading of the description, it will be noisy. You know how cozy means small in real estate. well "This apartment is located in a bustling and vibrant area. The owner has installed all double paned windows to help reduce noise, but some may still be sensitive to it." means noisy. This apartment is more spacious than the other and that second bedroom is great. Tough decision in my opinion, especially when you consider that it does not appear to have a registration number but it does seem to have AC which could be a major benefit.

One thing I did before renting an apartment in Paris, where we are now, is try to find the street it is located on and "drive around." I do this on street view on Google maps and get a feel for the area. Agree that both areas are great for atmosphere and walking around but the one does seem to indicate noisy, which after being out walking, can be a real problem. Transportation, the metro and buses, are everywhere and it all can be managed when looking at the maps. The second apartment has a better kitchen if you plan on using that and nice to have the room to spread out a bit when relaxing. Enjoy!

Vacationinparis.com is inaccessible from my French IP address: this makes me suspect that the listings are not guaranteed to be legal. I could not access your link.
EDIT disregard the above, just a device issue apparently! I got through on another phone :-)

The other one between Rue de Turbigo / rue Saint Martin is in a great neighborhood, I live 1/4 mile away so I can attest to that. Edge of the Marais, good métro connections, plenty of good restaurants in the vicinity.

Honestly there's no way to tell if ANY apartment is "legal" which is one reason I go with an agency over Air BnB . Yes I know, "look for the 15 digit number" But... 1483395446034238 means "look I have 15 digits" But they could be just what I typed... 15 digits I made up. Unless there's a way for the renter to go to some data base and "validate" then the "registration" code is window dressing. Not to mention that you have no way of knowing how many days the owner has rented of their allowed days. That said agencies often have more units and can move you if there is an issue and having had a refund from Vacation in Paris when I had to cancel and having had to FIGHT with AirBnB when the owner cancelled I would just perfer an agency :)

( I also have a very good reason to believe that one of the "top rental agencies" that gets great reviews on a lot of social media etc... is making up their numbers, but ... i don't think I dare post details about which agency.. they are rather aggressive in defending their reputation. A friend had a bad stay and wrote a blog post about it and got cease and desist letters from attorneys even though she had "proof" she had to get her attorney to tell them where they could take their letter :) Don't want to drag Rick into their drama But the registration number validation came up in the "discussion" and as soon as it did the agency disappeared Hmmm....)

I'm using a French IP, too, Balso but can access both websites.

Note that the second apartment has two living rooms, the second one having the sofabed. So both apartments have two separate sleeping areas.

Again, like JHK, I flag the wording "some people might be sensitive to noise." To me this equals "this apartment is noisy" but the wording puts the responsibility onto the renter. Always beware sleeping areas facing the street, much less on a first floor. I wouldn't rent a bedroom on a low floor facing the street. I regularly stay with a friend on a fifth floor (6th US)facing the street and sometimes get awakened by the bartenders across the street cleaning up at 4am.

So, regarding the Vacation in Paris one now... AC sure is nice to have, but noise warnings should be taken seriously as Paris apartments do get pretty loud when they're in the wrong place. It depends how sensitive you are.
The location is a bit closer to most sights (only a bit!) but being more touristy it has less of a local flair these days.

Hi fro Wisconsin,
Their 1st floor is our second floor. remember that. As an reasonably fit 70 year old, I want an elevator if I am above our second floor. After a day or morning out to come back and look at those stairs...ouch. And if you wanted to go 'home' and rest for a while before going out for the evening. Ouch. Read reviews about the elevator, small is not a problem, they are. Doesn't work...ouch.

Second is AC. Third is quiet.

wayne inWI

Try earplugs and you don't have to worry about the noise. Get the silacone ones, they are the best.