I'd say, in this Japan vs. West talk, that for me that SEGA style is very much what Aki has said:
variety. You can't peg SEGA down to one style, and therein is the SEGA style. I would also say the SEGA style is
originality.
Only SEGA can give us cartoonishly cute Sonic games, trippy NiGHTS, sci-fi fantasy Phantasy Star, hardcore east meets west Shinobi, funky graffiti inspired JSR, Sakura Wars, Panzer Dragoon, Daytona... the list goes on. All of these are SEGA, but no two are exactly alike. That is why I love All-Stars Transformed so much, it really nails this variety. Just look at the cast roster image of all the racers in ASR, what an eclectic mix!
I would say a large contributor to this style of uniqueness is the fact that SEGA is both Western and Japanese. Sometimes games contain influences from both regions (Shinobi, Sonic, Daytona, HotD) other times they remain rather exclusive to influences from one (Ecco is very Western feeling to me, as is TJ&E, Hell Yeah, Football Manager, Total War)(JSR, Sakura Taisen, Phantasy Star) feel Japanese. Yet, even then, there are elements of the other like I mentioned with JSR.
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That's why I love SEGA. You could only play SEGA games for the rest of your life and you'd get such a great amount of variety, and it never would feel samey or stale.