360 gen was overrated. Massively.
Sure, it started out well but if you actually look and see what came out of it, there's remarkably little that's stood the test of time.
It went particularly well for MS for a bunch of reasons, Japanese games falling out of fashion, online multiplayer being the new hotness, being the first to capitalize on the Indie-game breakout, Sony being slow out the gate and devs struggling with the arcane PS3 hardware, etc.
Whats the common thread with all those things? Simple, every one of them had fuck all to do with Xbox itself. They were either external events or the result of them being better positioned to reap the benefits of these market shifts than their competition. Basically it was either inherited from the plan/design philosophy behind the original Xbox, or dumb luck.
Hell, the one tentpole franchise they established was Gears, and that was Epic's baby. The nearest, best to that Crackdown started out on the original Xbox and only really sold thanks to it being bundled with the Halo 3 beta pass.
When they did try to react to the market, what came out of it was... Kinect. Hell, people may have sniggered at the goofy looking move wands but at least they proved to have some lasting value thanks to their convergence with VR.
Looking back, the overwhelming majority of big titles were multi-platform offerings from western third-party developers. Most of which didn't so much become synonymous with Xbox because they ran better on that platform, but more that they ran considerably worse on PS3. This is an important difference due to the PS3 being, when utilized properly, more than a match for 360 and the performance defecitr being the result of them being unwilling/unable to tailor their engines for its oddball architecture. In essence, although this may have been a "win" at the time for MS, it wasn't a direct consequence of their actions, they just benefited from the circumstance.
The irony is that Xbox didn't get lazy with the Xbox One. They'd already settled in that particular rut within the first few years of the 360's life. People just didn't notice because the competition was either struggling (Playstation) or off doing its own thing (Nintendo).