It really depends at what age you asked me about what Pokemon game I wanted. While I was the kid who always ended up having both versions eventually, by having siblings around my age also into Pokemon, I would choose my versions differently based upon a few different factors.
For example, when I was very young, I would always go with what color, or metal, I liked more. This was also in combination of what was on the cartridge itself. So, I got Red versions for myself because I liked the color more and I liked charizard more. Ignore the fact that my first starter was Venasaur though.... My sister picked blue in comparison to me. When Gold and Silver came around, I went with Silver since I liked the color more, and I actually thought Lugia looked really cool. Also ignore the fact that I like Ho-oh more now as well!
Eventually as I got older I'd start to look into what exclusives each version had as well. Like, when Ruby and Sapphire came out, I picked Sapphire for not only having Kyogre, but also because Seviper was the exclusive in it as well. Ignore I like Zangoose more now too.
This trend would really continue, however, the last game I actually bought new was Ruby and Sapphire. I skipped several generations until Black and White 2 came out. I restarted with Emerald and sort of caught up from there usually going with the third version first, and then playing the original releases second. This has led to some interesting comparisons, like playing Pearl after playing Platinum, and realizing that I can't stand how utterly slow Diamond and Pearl are. For X and Y, it was picking my favorite of the two legendaries, and that was easily Xerneas. Topically I actually preordered Alpha Sapphire for nostaglia reasons today, since, I had Sapphire first, and, I can easily get a Zangoose from the GTS or trading one over.
While I don't really have a 'favorite version' these days, I still will list the versions I would of picked.
Gen 1: Red
Gen 2: Silver
Gen 3: Sapphire
Gen 4: Pearl
Gen 5: Black/Black 2
Gen 6: X