I definitely get where Esteban is going, because for me my first memories of playing Neo Geo games were of Magician Lord and Ninja Combat, basically. If I got lucky I'd see Robo Army or Mutation Nation which I also liked. Usually you'd get a sports games too, Neo Turf Masters I guess but I was too young and dumb to realize I liked golf at the the time. Baseball Stars sometimes also. (I happen to really like Baseball Stars 2, btw - toss up between that and Basewars for my favorite baseball game ever and I don't even really like sports that much.) Sengoku was one of my favorites, I didn't see it that much but I did have a solid couple weeks with it on a camping trip once. At the time it was just so weird and different. I have to say I don't think I ever saw any of the shooters in a MVS growing up at any point, I think because there were so few.
(Neo) Fighting games didn't really catch on for a while in my memory.... like I remember seeing Fatal Fury (the very first one) and maybe Art of Fighting, but only after a while. I don't think anyone really cared about them really until Samurai Shodown came out, and even then I remember SS2 being the big hit. Fatal Fury Special was somewhat popular around the same time also. When KoF 95' came out that definitely had a following, but nobody (at least around me) paid a lick of attention to 94' (before or after.) I think it's here the popularity started to snowball for VS fighters. (And mostly of course from SF2 and Mortal Kombat I'm sure). I am not a huge fan of fighting games, but I have gotten into certain ones for small periods of time - I bought KoF 95' for the Saturn and later on Match of the Millennium for the NGPC, and I liked stuff like Fighter's Megamix as well. But I know damn well after I see all the characters, all the specials, and stages, I'm basically bored of most of them. So they have limited appeal. I definitely appreciate the spritework and artistry involved in the SNK fighters, and I think that is what has really stuck out for me as a lasting impression - they looked damn good. Nothing looked as good at home for a long ass time. If they were arcade only, we wouldn't have been as impressed I don't think as many games looked pretty nice in the arcade (but honestly SNK does deserve special recognition in this area.) but since it was possible to get these games on a home console, the comparisons to the SNES/Genesis/TG16 were inevitable - not to mention driven by magazine advertisements which we were all a little bit subject to since that was the best method of getting game related news pre-internet.
When I look back at the Neo library now I am somewhat disappointed that it has so many fighting games. I tend to like more "adventure" titles whether they be Action RPGs, Dungeon Crawlers, Survival Horror, or Metroid style games, but the Neo had to have games that could be used in an MVS or AES. So at best you got some pure platformers, none of which I remember being super great (Blue's Journey) or those early Alpha Denshi titles, or the rare shooter (none of which I agree stand out above the many great ones in the PCE's library). Still, a fair amount of decent non fighting titles exist. Metal Slug of course needs no introduction and Shock Troopers also comes to mind. And I have a soft spot for those Alpha Denshi (ADK) titles. But you do wonder what could have been done with all that power, to make games meant purely to be played at home. Of course the home system they knew was just a way to play the arcade games at home, the market for AES cartridges wasn't very large since it was beyond the affordability of your average family.
Oh and just for the record, my favorite SNK game is probably Card Fighter's Clash. Plenting of fighting game references, but a collectable card/strategy crossover game got a lot more time out of me than probably the time spent on all of their fighting games combined.