From a hardware standpoint, Neo Geo AES and MVS are exactly the same. The games for each version are identical in every way. The difference is that the MVS arcade hardware was meant for commercial use, and was initially much more expensive than the AES versions (about 600 bucks for an MVS kit for each game). The AES was meant for home consumer use, and the games were cheaper originally (around $200 for each game). Since the games were identical on each version, SNK made the board sizes inside the cartridges slightly different, so they wouldn't fit each other and arcade operators couldn't purchase the cheaper AES versions for their cabs.
But there were a lot more arcades with Neo Geo MVS machines than rich kids with Neo Geo AES home consoles, so over time the AES versions became more valuable on the secondhand market since they're more rare.
There's no getting around it: the Neo Geo AES is the most expensive video game console in existence to collect for. I had around 25 games at one point, but prices went crazy and I sold them to pay for my wedding.
It got to a point where I wasn't playing them for fear of damaging them.
The MVS isn't exactly cheap to collect for either, but it's slightly more manageable. The prices for MVS carts have gone up in recent years due to the rise of "consolized MVS" units, which are the guts of a 1-slot MVS arcade machine transplanted into the form of a video game console. The idea is that you get the home Neo Geo experience without having to hunt down the insane rarities (and dubious bootlegs!) of the AES scene.
Consolized MVS makers include:
https://www.arcadeworks.net/omega-neo-geo-mvs-home-consoleand
http://www.analogueinteractive.com/pages/analogue-storeOne final note of pros and cons:
MVS
+ All Neo Geo games were released for it
+ Arcade cabs look awesome
- Expensive
- Carts are kinda ugly
AES
+ The coolest home console ever
+ Cartridges and boxes are beautiful
- Not all Neo Geo games were released for it (but most were)
- Beyond expensive
- Some games are so rare that there might be less than 10 in existence
Neo Geo CD
+ Cheapest way to play Neo Geo hardware
+ Some games have enhanced CD-exclusive soundtracks
- Nearly all of the Neo Geo games after 1997 are unavailable for it
- Long loading times