As far as the Yamaha EZ-200 versus EZ-220 are concerned, the main differences appear to be the types of connections and the number of voices:
EZ-200 has MIDI In/Out connections but no USB connection
EZ-220 has USB-to-Host connection but no MIDI connections
EZ-200 has 375 voices-- stereo grand piano, 361 XGlite voices, 12 drum kits, and 1 sound effects kit
EZ-220 has 392 voices-- stereo grand piano, 361 XGlite voices, 17 XGlite option voices, 12 drum kits, and 1 sound effects kit
The EZ-220 also has the ability to work with the "EZ-220 Page Turner" app on an iPad, which displays the "sheet music" (in electronic form) for the MIDI song file you're playing and automatically turns the pages to keep up with your playing.
By the way, I have no familiarity with either one, so I downloaded their owner's manuals from Yamaha's web site. I recommend doing that for any keyboard you're interested in, along with any other documents (e.g., sometimes the list of available sounds will be given in a separate document), as it will let you read about the keyboard's features and how to use them; plus there's usually a summary of the keyboard's features and specifications near the back of the manual, which can help you compare keyboards.
As far as the Yamaha EZ models versus the Casio LK models are concerned, I haven't tried to see what all the differences are, but one difference is that the Yamaha EZ keyboards have a maximum polyphony of 32 notes (or 16 for some sounds), whereas the Casio LK keyboards have a maximum of 48 notes (or 24 for some sounds). That may or may not be significant, depending on your needs.
Aside from that, some people think that Yamaha keyboards sound better than Casio keyboards-- although this can be largely a matter of personal opinion or preference. I have an older Casio CTK keyboard and two newer Yamaha PSR-E keyboards, and the two Yamahas do sound better than the Casio for the most part-- however, this is at least partly due to the age of my Casio, since Casio's newer models sound better than their older ones (which is also true of Yamaha), given the technological advances.
With respect to sound, you'll just need to visit a music store so you can play the Casio and Yamaha keyboards side-by-side to compare them and see whether you can tell any difference or which you prefer. Different people have different "ears" when it comes to music and sound, so you might think that two keyboards sound the same whereas someone else might think they sound totally different, or vice versa-- so you really need to hear them for yourself.
The same advice is true for features-- you'll just need to do a feature comparison of whichever keyboards you're considering, and decide for yourself whether a specific feature is important or unimportant to you.
Having said all that, I do have a few comments.
First, I personally think it's (usually) best to go with a newer model rather than an older model, because the newer model is usually going to have the greater number of sounds (Casio = "tones," Yamaha = "voices") and features, as well as overall improvements in the technology and design. There can be exceptions to this, such as if both models are more or less identical other than, say, the number of sounds, in which case the older model might be a better buy if the price is discounted. Another exception can be if an older model has features or sound-generation technology not found in the newer models, in which case the older model might be desirable for that reason and may even be more expensive (e.g., if it's considered to be a hard-to-find collector's item).
Second, for your purposes I expect you'll want a keyboard that has a USB-to-Host connection, since you want to use the keyboard with Synthesia. For example, if you get the older EZ-200, you'll need to get a MIDI-to-USB connector to connect the keyboard to your computer since the EZ-200 doesn't have a USB-to-Host connection. But in other situations you might prefer to get a keyboard that has MIDI connections so you can connect different keyboards together. It depends on your specific needs and plans.
And third (and lastly), you might want to get the cheapest lighted-keys keyboard you can find for learning/practicing purposes, then buy a better non-lighted-keys keyboard that has more features and voices for performance purposes. Again, it depends on your needs and plans. You said "Synthesia + Lighted keys looks like an idiot-proof way to play keyboards, live, without screwing up too much," but I'm not sure what you meant by "live." If you're talking about performing on stage, I'd personally go with a dirt-cheap used lighted-keys keyboard for learning on, but buy a better/newer/pricier non-lighted-keys keyboard for playing on stage. But if you aren't planning on performing on stage per se, and would prefer to buy just one keyboard that will serve you well for at least a few years, then I'd personally go for whichever lighted-keys keyboard has the most features and sounds.
But I agree with Gary/happyrat1-- lighted-keys keyboards are essentially a gimmick. And I'd even go so far to say that the same is true of programs like Synthesia, Piano Booster, and the "music education" features built into some Casio and Yamaha keyboards. That doesn't mean these things aren't helpful for some people, but for myself it's usually simpler, easier, and faster to learn to play a song by ear (I can read music, but I've always preferred finding the right notes by just listening to them). By all means, use Synthesia and a lighted-keys keyboard if you want, but try not to rely on that approach-- and consider buying the cheapest used lighted-keys keyboard you can find for practicing on, but spending a good bit more on a better keyboard for actually performing on.
