Which Madrid Museum on a Sunday Afternoon?

All three of these museums are within a kilometer of each other, and the Reina Sofia is practically across the street from the Atocha station. The Prado and the Thyssen are across the street from each other, and all three are absolutely magnificent. I'll be in Madrid in late October for a short visit, and I'll only have time for two of them - but, I'll be back in February - so my plans will be somewhat like yours.
My own preference is for the modern, so I slightly lean toward the Thyssen and Reina Sofia - but my love for the Prado is such that when I go - it's an all day visit.
Will the Reina be crowded? Yep, probably. So what - you are seeing Guernica! Stand around - wait a bit - the crowd moves out and you will be in the front row. Is the Prado crowded? Sure. Same deal. My experiences have been that the Thyssen is less crowded than the others as it seems to be the museum most likely to be skipped. Big mistake. It is fabulous!

I’ve been to many art museums and Guernica is the most moving piece of art I have seen. Loved the Prado.

I did the Madrid museums in late May 2016 and am sure they're more crowded now. The only crowd in the Reina Sofia was in front of "Guernica", but I wandered through the rest of the museum and returned to a nearly empty room.

The only pictures at the Prado with clots of people in front of them were "Las Meninas" and Bosch's "Tree of Life". The museum was busy (multiple people in each room), but you could pretty much walk right up and stand in front of any other painting at will.

The Thyssen was not busy at all and does seem to be the forgotten one.

Someone once suggested that it may be easiest to see the most popular pictures during the lunch hour (perhaps 1 PM to 4 PM in Spain?), when tour groups are likely to be elsewhere. That's not a bad idea, because tour groups tend to stand in front of each key picture for several minutes, blocking others' access. A similar number of unconnected travelers will come and go, offering an opportunity to improve your position.

Obviously you have to see all three, with the unified ticket option. Note that number four, the Real Academia de Bellas Artes de San Fernando (near Puerto del Sol) has a remarkable, massive, collection and is rarely crowded. It may be the most overlooked attraction in Madrid.

I was in Madrid on a Sunday mid-Nov 2017. I did the RS & TB that day and didn't get the museum pass as RS is free on Sunday and the museum pass doesn't cover the TB special exhibit I wanted to see - Toulouse Latrec.
I would leave the Prado until next time (and maybe a return to the TB as with its growing modern art collection, your timing may not be enough to see the entire museum and any special exhibit).
Both were more crowded than the Prado was mid-week because locals were there as well. I did the TB first and RS at end of day. There were more university students at the RS but I wouldn't call it 'extremely crowded' (and I expected worse). I don't care much about the crowds as they ebb and flow, so just wait a minute and people will pass. Also, at 5'8" I may have a little height advantage.

If you are an emotional type that cries at TV ads, take tissues for the gallery of photos of the war that lead to Guernica. These moved me much more that Picasso's representation. Despite all of Rick's explanations and trying to be open minded, I just don't get it. I think the Dali are on the same floor, so you could bypass the rest if you want.
So, I guess I would say do both the RS and TB, but the TB last as you may find it too extensive for one go. What I didn't realize was how the collection is displayed. For one thing, the fact that it is a single independent collection is mind boggling. It is arranged by centuries leading into Impressionist then modern, but in amongst the old masters, there are modern installations which are kind of fun and I wouldn't want to miss....so maybe you could do it in 3 hours, but I have the feeling the RS has some appeal for you for this trip. Weather may dictate how much of your 'strolling' El Retiro you can do. It's a lovely park but much bigger than I anticipated and not as close to the museums either (unless you focus on just the back end - which the locals do not). You might want to consider the botanical garden instead. It is beside the Prado, I think entry is 3E and there are conservatories as well as the garden beds that were still of some interest mid Nov. I am a bird watcher, so I had had two hobbies going on in one location.

The consensus of many Art historians is that the Prado is one of the top candidates for the best art museum in the world for European art to the mid-1800's. There are several reasons for this, which you can explore if so inclined.

So, one question to ask yourself: if you're in Madrid, and are inclined to go to an art museum or two, why not the Prado? (There's probably no right or wrong answer.)

The Reina Sofia is admission free on Sundays between 1:30 and 7:00pm. There may be a line prior to it opening, but after the initial rush is over, it shouldn’t be overcrowded. I’ve been to it twice during the free hours, once on a Sunday and once during the evening hours, and didn’t have more than a 10 minute wait to get in. If this is your first time visiting it, you’ll probably want more than two hours to see everything. On my 2nd visit, the two free evening hours was more than enough. There’s no reason to pay €10 on Monday what you can see for free on Sunday; it won’t be any less crowded.

The Prado would be my choice as by far the most impressive of the three and then focus on great Spanish artists.

If you have never seen Guernica and also don't have much museum interest then the Reina Sofia just to see that might be a good choice.

Based on everyone's recommendations, I think we'll go ahead and go to the Reina Sofia on the Sunday afternoon during the free hours, go to the Prado on Monday morning, and we might try to fit in the Thyssen-Bornemisza on our jet lag day a few days earlier if we are up for it. Thanks all!