Madrid - La Latina or Sol?

I'm not acquainted with either hotel, but all things equal, I would chose La Latina and Calle Cava Baja, and for the reasons you cited: a charming old area, not quite as "touristy" as Sol, with several local cafes and tapas bars. I haven't actually lodged in that neighborhood, but would probably seek to if I were not already committed to a great guest house in the Huertas neighborhood. But when I visit Madrid I still find time to wander around the La Latina area.
On the other hand: My last visit to Madrid was in 2019, but if your visit this November is typical of the several November trips I've made, you will probably find the area around Posada del Peine to be rather busy, but still a good area to stay in, and certainly a convenient one. Nearby Esparteros street has a couple of tapas bars I like which, though a bit plain, seem quite local in character (at least one has a restaurant in the back room), and where even at the bar you can get a "racion," which along with a drink and the associated tapa, makes for a reasonable meal, if not an overly nutritious one. There's no doubt that the Sol area is more touristy, but the Madrileños seem to enjoy the area as well, and though I haven't done a scientific survey, it seemed to me that the locals dominated the area in November.
So briefly -- based on location I personally would choose La Latina, but if shorter walks are a priority, the Sol area will be fine.
(This need not affect your decision, but you may be interested in knowing (if you don't already) that La Latina was named after a female scholar of the 15th century, Beatriz Galindo, who was such a noted Latin expert that she earned the nickname by which the neighborhood is now known.)

Which sights are you planning to visit? I stayed at Sol (twice). It's a downhill walk to the Prado of about 1 km, which means uphill going back. It's not terribly steep, but neither is it a gentle slope. The Thyssen is a little closer. AFAIK there's no metro near them. Traffic was pretty bad when I was there about 8 years ago in winter. I don't imagine it's got much better, which means if the walking is tough, buses and taxis may be very slow. I don't remember much of the topography, but I did that walk at least 8-9 times on my two visits.

If you want to be by a couple sites, then select Petit Palace Posada Del Peine. We stayed at it back in 2019 after walking part of the Camino. The room we had was a little small and I didn’t care for the tinted glass wall between the bathroom and rest of the room, but the included breakfast buffet was great. On that trip there was a world medical convention going on in Madrid and prices for hotel rooms were 3X the normal rate, so we got the cheapest room possible. The hotel is a couple minute walk from from the Sol metro stop and right at the Plaza Mayor. It’s probably a 20 minutes walk to each, the Prado, Reina Sofía, and the Royal Palace. We normally stay at Hotel Europa right at the Puerta Del Sol, but on that trip because of the conference, it was too costly. We like sitting at the cafe by the hotel to people watch. There is no cafe right at the Petit Palace.

The other hotel is away from the main tourist area and sites, and may be somewhat quieter.

I've stayed in both locations and prefer La Latina. We stayed in a flat on Calle Cava Alto, one block off Calle Toledo. Absolutely LOVED the location. At the time the Latina metro stop was closed, but it had zero impact on us. Lots of restos, bars, shops in the area, it seems like a place you'd want to live if you lived in Madrid. Sol was interesting, but much more touristy.

The difference is much greater than the distance—I know the neighborhood well, and I’d stay on Cava Baja.

We stayed at the Hotel Europa in April, just before Palm Sunday weekend.
The location is great, right at Sol. 1 minute to the Metro.
The hotel was under construction on the Sol facing side. We had a room with a balcony and the soundproofing was excellent.
Hotel staff was extremely helpful.
Walking distance to many sights and places. With all of the stops we made, it took us 3 days to do Steve's 90 minute walking tour.
Yes, it's a touristy area but we found excellent restaurants and a fab funky tapas bar - Rosi La Loca.
We brought Hot Chocolate mix from Chocolateria San Gines to friends we were visiting outside Sevilla and they loved it.
It's a great location for easy sightseeing.
Definitely recommended.