I've been to both Museums albeit on separate occasions and there is not really much to say about them which you probably already know, as it sounds like you have done research and checked out the website.
The only surprise really we had was that the food options onsite were not so good and expensive (although we had a toddler with us which limited us a bit). If I go back I would take sandwiches with me. There is also very little close by to either Museum, although if I recall correctly there is a Subway Sandwich place close to the Sinsheim museum if you have a car.
I preferred Sinsheim, but I guess it depends on what exactly you want to look at.
Unless you really take your time then you don't need a whole day for each, 4 -5 hours is enough. In fact, as there is only 30 mins between them if you pushed yourself you could even probably do both in a single day. Although this might not be as enjoyable, and I wouldn't suggest it in your case.
I would suggest to look around for hotels, there are plenty of options around the area, and you might find it better to stay in or close to a city centre so that you have more options in the evening for eating and drinking.
I suggest that if you have time you go into Speyer itself, the Cathedral is nice.