Xbla is fantastic. But I don't think it's that good enough to make 360 jump out to "best system ever", but then, the subject of "best system" is subjective. PSX is my favorite system, though I feel ps2 is better. I can see why 360 would be someones favorite, after going on 8 years of playing on the thing. That's a long ass time.
You are also right, 360 does have more in the way of say, fighters. Fighters were entirely revived this gen. But most of those action, fighting, and shooting games are available on other platforms, namely the playstation 3. There are exceptions, mostly xbla titles like MotW, Rez HD, Ikaruga HD;etc only available on xbla. But they're still ports. You said to ignore psn/xbla games, and imo, those are the only major qualifiers for BOTH systems. I found both dd services had more games that appealed to my tastes than anything on the mainstream market - for the most part. Yet, the dd titles are the ones that were mostly exclusive. That mostly leaves retail titles. Maybe I'm ignorant on 360 library, but pretty much every major fighter is on ps3, and the major action games of this gen (Bayo, DMC4, NG2, Vanquish) are all available on the ps3 though some of those versions are not optimal they're still available. Shooters, I'll grant you. 360 mopped ps3 up with 2d shooters.
For reference, my favorite dd games this gen are Outrun 2 HD, Mega Man 9, and Hard Corps Uprising. All of which are also on ps3. Though, I owned them on the 360 and not on ps3. To me, it's like saying ps2 is such a great system because it has Prince of Persia: Sands of Time, Beyond Good and Evil, and SSX3. All of those games are on the other consoles, and none of those games go into why ps2 was such a great system: exclusives. You played the ps2 because it had all this shit you couldn't find on gc and xbox. You play your 360 and neglect your ps3 because, for the most part, both systems have an almost 1:1 ratio of game library. Practically all of the major games this generation have multiplatform. What's the point of playing a ps3 when you've got an Xbox 360? Exclusives. It will always be down to exclusives, and exclusives aren't that important these days and are becoming more and more rare.