Brussels to Paris train - seeking advice on deciding which one

Better depends on who you are and what you prefer, but here are my thoughts:

Question here is how difficult is this transfer?

Very easy, it is roughly a 500 m walk between the station. But, if it was my trip I'd spend a few hours in Lille if choosing this option.

Will there be sufficient time to hop on a train on this route with a
9:40 pm arrival at Gare du Nord to the Odeon metro stop? I would
imagine so, but I ask just in case, because we would have to purchase
the Navigo Easy cards and load them before trying to get on the Metro.

You can buy the metro tickets onboard the Thalys and save a bit of time.

Europe to Flandres station in Lille is an easy transfer on foot, but 20 minutes is tight so don't dally.
In Paris, if somehow you miss the last metro on line 4, you can take RER B to St Michel-Notre Dame followed by line 10 to Odeon, or line 5 to Austerlitz followed by 10 to Odeon, or 2 cabs (unless there is a van that can take 6 passengers).

Be careful taking a cab from Nord -- this is the one spot where travelers report scammer cabs in the cab line. If anyone tries to assert a fixed price, they are cheating you. You must run the meter for a fair ride. The fare on the meter is good for 4 people -- it is 4 Euro a head for passengers 5 and 6 in addition.

There is no danger carrying a suitcase on the street at 10. 10 or 11 is when people are getting out of dinner.

If you know the layout of Lille-Europe and Lille Flandres, and their relative distance from each other, 20 minutes might be okay, but it would make me nervous, and I do know both the stations and how to walk between the two.

I wouldn't attempt it if I had to do it without ever having been there before.

I agree that 20 minutes is pushing it. I've used both stations and know the route between - it is pretty simple but for a newbie and luggage I'd worry.

I don't mean to twist your arm, but it's worth considering changing your sleeping town to Antwerp (which I personally prefer) from Brussels, but preference isn't the issue: Train schedules from Antwerp to Paris are different, so you might have other options. Just an idea.

I understand that appointments for scarce resources are necessary, but I don't like the pressure of the Versailles tour. Is that a Versailles product, or a private guide? Is your whole Paris visit that tightly scheduled? You are vulnerable to pedestrian traffic at the arrival train station, and to broken-down Metro ticket vending machines. (I know you plan to take a cab, I'm just saying.) What if there is a line to check-in for your hotel? What about the RER to Versailles, which is not a short trip? Then you have to get from the RER to the palace. This part of your day seems under-researched.

Paris is a very safe city. That said, I always use a belt-pouch in Europe. Your personal safety is not an issue at 10PM. As I remember, the link between the two stations in Lille is a covered corridor, so you're not even exposed to rain. Just to be sure, as long as you might change trains anyway, have you checked conventional trains, or only the premium services?

Thank you all for your responses!

@Tim I have been trying to make this trip for two years, originally scheduled for 2020. I have researched quite a bit. The Versailles tour starts in Paris (Invalides area), we are booked with Take Walks. We had credits we needed to use, the rest of Paris we will see on our own at a leisurely place, with reservations only for the Louvre and the Eiffel Tower. Of the six of us, four have already been to Versailles. When I went, we used the PMP and spent about half a day there. We went on our own, on the train and saw everything we wanted to see. That was on a weekday in September, so we did not get many crowds, and did not have to reserve. This time we are going with parents and teens. Because parents and us have been to Versailles previously, I chose to take a guided tour that leaves from Paris at 1:45 pm (and goes by train).

Regarding the stay in Belgium, its easier for us to stay in Brussels. The train ride will be shorter from our long haul flight, and also its easier to take a train to Paris. Based on all of the feedback, we have decided to take an evening Thalys train to Paris.

Thanks for sharing the additional logistics of your planned journey. I presume you learned that the Thalys trains only leave from Brussel-Midi/Zuid, and not from Centraal. There is no extra charge for a local train from either of the other two downtown stations, but there it does make a train change necessary.

Having a tour company in Paris may be helpful if there is any change in French Covid documentation rules at the time of your actual trip.