Protip: The 360 offers an optional install, install the games onto the hard drive to save from wear & tear and slightly improved loading times.
I've learned that it is night and day in some cases. Lost Odyssey benefits a lot for instance.
Most are like what you describe though, slighly better loading times only.
And some, are actually worse, I remember GTA5 installs to HDD always and uses both DVD read streaming and HDD Streaming, so if you install both (?) you create a streaming bottleneck.
And yeah, when I bought my Series X, I was expecting to be able to play most of my 360's library. Didn't take long for me to realize that I had to plug my 360 back on my TV. Can't play Soul Calibur IV-V / Dead or Alive 4-5 / Most SHMUPS / PGR 3-4 / Ridge Racer 6 / etc on a Xbox One/X/Series S/X.
Yes, I skipped Xbox last gen, but when I bought a Xbox One S for my girlfriends youngest, who is crazy about racing and shooting games, I assumed I could offset Forza 6/7 price by giving/borrowing him Forza 4 and PGR4, no dice.
That made it so that the console didn't end up as cheap as I originally thought because I had to buy Forza 6 (better than 7 for offline play, I concluded - also cheaper), then Forza Horizon 4, but... Seeing how the kid treats his games, means my Forza 4 and PGR4 copies are safest with me.
Xbox 360 BC is a really nice to have and with kids in tow you know you can just get some games on the cheap, graphics are still good enough and games are cheap. I think I bought,
Battlefield Bad Company 2 (great campaign, online is still on, well regarded),
Call of Duty Modern Warfare 3 (it was like 3 pounds, kid played on easy and beat it in one day
, but still likes to play the deathmatch co-op thing),
Bioshock Infinite because it was cheap and why not and
Darksiders 1, because seeing there is a "HD remaster" the older HD version is just so cheap and kid likes brawlers. Ah, and lastly but not least,
Saints Row IV, also really cheap.
All this must have been less than 15 euros. I still haven't sourced a copy of GTAIV because it sells for roughly 15 euros, which means a lot of other games.
If Xbox One S didn't have X360 back-compat kid would have like 25% of the games he has. And, if Xbox Series S read discs and had full X360 compatibility, I would buy one here and now.
I should also note that, on the Xbox 360 store:
- Crackdown 1 and 2 are free! (Someone mentioned Crackdown in this thread already)
- Too Human is free as well (supposedly meh game, but some might enjoy going through it - I'm kinda amazed it wasn't delisted)
- Resident Evil Revelations 2 for X360 is free too. This is the full game, not the first episode (on Xbox One and PS4 you get the aforementioned first episode only, so a demo) - I'm not sure why is it free, but it's been that way for years.