I feel like the 360 is THE xbox console!
Personally the 360 (imo) battled the PS3 very fairly in terms of console wars whereas the generation before it, heavily favored the PS2.
The 360 had several games that made it a cornerstone in it's era of gaming with the likes of the GoW: Trilogy, Halo 3 & 4, and also by securing DLC earlier for AAA-game series CoD shows it was ready for the big leagues in the exciting console war!
The 360 also showed the capability of online functionality and was the gold-standard for years!
The 360's legacy could be bogged down by it's technical shortcomings, but after the sand has settled, there's a reason many people bought a second (or third) console after their's has previous RROD! Cheers!