I will ignore the likes of the Amiga as homebrew on an ostensibly open system... yeah.
Homebrew is more than emulation to me. Indeed emulation is but a tiny fraction of it all. I like emulation but it is a trivial thing these days (was back when as well but for ease of use a hacked console represented something). On the flip side remakes of old games is a different matter.
Anyway that leaves 5 main contenders. Backwards compatibility + a bit of token extra stuff I am ignoring, and none of them make the experience so much radically better that it gets hard -- none showcase stuff like that fancy mode 7 filter or high resolution rendering or anything like that.
Xbox, GBA, DS, PSP, Wii.
No other device has seen the levels of creativity and drive to make cool shit as those devices. I have serious doubts we ever will see it again either as somewhat open devices reign again and I can't see a nominally closed device overcome that, nor having interesting enough hardware to justify it.
The wii was a bit of an anomaly. There was some good homebrew beyond emulators and systems management but not as much of it and it did not do as much as the others. What homebrew it got often struggled to shed the tech demo... I am going to say stigma but want a better term than that.
The xbox had xbmc which was a complete game changer for a lot of things. After linux though it was mostly emulation that drew people in.
The GBA. Did very well here and set the stage for what was to come but has been overshadowed by the DS and PSP. That said there are still some absolute gems in its homebrew catalogue (
https://gbatemp.net/threads/links-to-various-gbatemp-features-over-the-years.352851/ features a few and notes more in passing).
DS vs PSP then. On the emulator side of things the PSP won overall but most of that was "I'll port this old PC emulator as C compilation is a thing that can be done here" which contrasted with the GBA/DS approach of tightly coded emulators doing good stuff. I dismissed emulation already. The PSP's extra power allowed it a more or less fully realised version of SDL which helped a lot of take off, and its extra power was put to use on many occasions to do things the DS could not. On the other hand the DS' touch screen did a lot for it, and what the DS did get was often very fun and put together with the DS in mind, plus all the ports of various protocols.
If you had a DS and PSP while they were active then you probably would have had the best time in homebrew on any device.