Pompeii or Herculaneum or both??

A day trip from Rome is long and exhausting. Have you considered Ostia Antica?
If you are set on Pompeii / Herculanum, the choice is tough.
Pompeii's extent is impressive, but also challenging if you cannot walk longer distances. The train station is right outside the entrance, which slightly alleviates this potential issue, but not fully.
Herculanum is several times smaller, but structures are better-preserved. You do have to walk 1 km round-trip from the station to the entrance.

Even if you were a speed walker, doing both in a day would be a rush. I preferred Pompeii over Herculaneum however since you're coming from Rome, I may choose Herculaneum because it is closer. As the above poster mentioned though, the walk to the entrance is about 1km downhill.

Pompeii has some of the world's largest cobblestones. They are challenging and tiring to walk on. There are often sidewalks, but they are mostly if not entirely way, way higher than the cobbled streets. When you need to change from one to the other (at an intersection, or to get around a clot of people), it isn't easy if you're short. And hopping down from the sidewalk onto a rounded cobblestone can be risky. You might want to Google photos Pompeii to see what I'm talking about.

I agree that it's a long trip from Rome to either Herculaneum or Pompeii, but Herculaneum is closer to Rome, which makes up for the time required to walk from the Ercolano Scavi Circumvesuviana stop to the excavations.

I found Pompeii more interesting, because there were some mosaics and frescoes to look at. (I'm really not big on the excavations themselves.) A lot of the best stuff is in the Archaeological Museum in Naples, however.

Ostia Antica is a much easier-to-reach site when you're staying in Rome.

Trying to see both in one day from Rome will make for a very, very long and hard day. Only you know the extent of your mobility proble, so it's really hard to recommendation one over the other. Just consider the fact that Pompeii will involve more walking and will be on more uneven surfaces than Herculaneum. As other have suggested, you might want to go to Ostia Antica instead. You can get there and back easily and quickly via public transit, and is, in my opinion, a much easier place to walk about. Just my opinion.

There might be some selection bias at play, but I have never seen anyone comment that they did this day trip and report positively. Having been to both sites while based locally, I cannot imagine trying to do this as a day trip, especially Pompeii. Pompeii is simply too big, too crowded, and usually too hot. If you’re day tripping in, you’re typically there during the crunch of the day. It’s just a lot to go through, and even in my best days this would knock me out.

Of course, both of these sites are spectacular so I don’t fault the attempt. Considering all factors, I would recommend Herculaneum if you were to pick one. It’s just as fascinating, but less iconic and therefore less crowded. It’s smaller and more manageable than Pompeii. I haven’t been to Ostia, but that’s recommended a lot and not just because it’s convenient.

https://community.ricksteves.com/travel-forum/italy/herculaneum-and-pompeii-questions

In case you don't know, Pompeii is right across the street from the Circumvesuviana commuter train stop. Herculaneum is a fifteen-minute steep downhill walk from its Circumvesuviana stop. So it's uphill on the way home. Pompeii has hot food inside, Herculaneum does not. It is easy to fill a full day with just Pompeii, although it's unfair to say that everyone should do so.

If you want to hedge your bets, you might consider a second train stop for Oplontis, a sort of Executive Villa. It's not very "like" Herculaneum, but it is very different from Pompeii. And it is quite important in Roman and architectural history. It's very small, and has more shade than Pompeii. There are two other sites, adding up to 5, but I haven't been to the other two.

Be aware that all of these places have worn, ridged, ancient ... paving stones. If you have weak ankles, or trip on pavement a lot, you should perhaps bring two walking sticks, or whatever works for you. I'm not trying to talk you out of it, just trying to avoid unpleasant surprises. All the sites are quite level, once you have entered them. There are a few stairs, here and there, many of which can be avoided. There is normally a long waiting line (standing still) to enter the Pompeii ... er, uh ... brothel.

Ostia Antica is much less known, but you might consider it. It is maybe 2/3 as good as Pompeii, but like Pompeii, it is also a huge ancient city that you can wander around and get lost in. It has intact multi-story Roman buildings, frescoes, latrines, taverns, tombs, baths, mosaics, a theater, the whole bit.

If you are starting from Rome, Ostia Antica is very easy to get to: it's a short half hour train from the Piramide station in the south of town. Once you get there, the entrance is a short walk.

Pompeii is very nice, but if you are starting out in Rome, it might not be a good idea to try to get there and back in one day. And even if all goes well in transit (a big IF), it will be super exhausting. And never mind doing Pompeii and Herculaneum the same day -- that sounds just about impossible.

Herculeum is not a difficult walk and there are lots of small places to eat all around the outside of the ruins. I found it quite interesting and less claustrophobic than Pompeii. Truly very interesting and easy to get to. Ostia Antica is even easier and is considered as Rome's first colony and is an easy train ride from Rome itself. Lots of mosaics to see, the "fast food" type restaurants that are also at Pompeii, places to see where the ground the wheat (why this place was so important to Rome). All 3 very interesting places but your time is limited.