Sadly, CRT TVs are pretty much hit or miss, Sony as well.
The differences between models can be sometimes marginal, additional inputs, PIP, additional speakers etc, but sadly the can often mean completely different electronics.
The two sets you mentioned have different types of chassis. The kv-24fv10 has the BA-4C chassis and the kv-xxfv300 a BA-5D. You could try to locate the service manuals for both of them to compare the two.
I personally dislike flatscreen TVs as they very often have geometry problems on the edges. They also are rarely consistently sharp, due to the very high defletion angle thanks to the flat tube. Also keep in mind that the chassis of both the TVs you posted are digital ones, meaning that you don't have analog potentiometers on the chassis for geometry adjustments and you have to do them in the service menu, which can be tedious if you change game systems very often. Putting an Extron RGB in between might help out in this case.
There is a general consensus that the late analog chassis of the Sony sets, especially the AE-1 models are highly desired. They seem to have the biggest game compatibility, as well as a lot of potentiometers for setting it up. You can read more about this particular model here: http://scarthunter.blogspot.pt/2012/03/its-bad-ass-sony.html
In fact i highly recommend reading the whole site, as it is highly informational: http://scarthunter.blogspot.pt/
Still, even if you find a TV with a fine chassis, the tube might still have burn-in or discolorations as well as other technical problems. So finding a certain model doesn't necessarily mean that you will be happy with the picture quality.
Also, keep in mind that as always, availlability is key. Sony sets are popular so a lot of people have access to them and hence recommend them. I have a 28" CRT made in Poland which imho, eats any Trinitron i ever had at home.
Sadly, you will have to buy at least a few CRT TVs before finding a model that you'll like.