I know, I get that alot :).
I just found SEGAs arcade approach more satifying, and I found alot of Nintendos offerings a bit... boring dare I say. But remember, I saw those games through the glasses of a fanboy, so I aim to revisit some of them :).
Oh trust me, when I was a little kid, I was definitely a "Nintendo kid", and I hated the Genesis, purely on the basis that other little kids who were "Sega kids" would talk shit about Nintendo, and say how their system was so much better. LOL
Such a sad thing really, as both camps were missing out. I do contend that the SNES overall had a better library than Genesis, and the NES to me is the best system of all time. BUT, in my teens and later adult years, I was able to try many Master System and Genesis games, and realized that, you know what, Sega really did have some great games too. So I hear where you're coming from. I'm sure if I had also had a Master System or Genesis as a kid, I would have liked it too. Hell, I had actually never even heard of the Master System, in the pre-internet era, until about 1992, when I got a special year's end holiday EGM issue that had a retrospective comparing all the consoles of the time (NES, Master System, Game Boy, Game Gear, Lynx, TG16, Genesis, SNES, Neo Geo). I had never heard of it because the small-ish town I spent part of my childhood in never had one in any of the stores.
Some of my favorite Sega games, or games that were on Genesis, are Golden Axe II & III (1 is okay but the sequels are better), Streets of Rage II & III (ditto), High Seas Havoc, Rockey Knight, Shinobi III, Columns III, Chakan (even though it's harder than fuck), and of course the Sonic games (Sonic 2 mainly).