Higan-performance would be far slower than either SNES9x or SNES9x Next.
SNES9x Next is a speedhacked and totally modified SNES9x 1.52 core - if that is still too slow for you the alternative perhaps would be a 1.43 core with some speedhacks - I don’t have that core yet as a libretro core and last time I checked SNES9x 1.50 on libretro, it wasn’t really any faster than SNES9x Next (in fact, the opposite with Yoshi’s Island spinning island screen) - and this is with the old APU that is supposed to decrease system requirements a lot.
For the record, I doubt right now you can find any regularly maintained version of SNES9x out there that would be faster than SNES9x Next. I looked for it before starting out with SNES9x Next and other than things like PocketSNES (which is butchered to hell and has numerous PPU bugs) there was really nothing out there. SNES emulation will probably always require higher system requirements than other systems.
With SNES9x Next I can at least guarantee that nearly all of the games except for Yoshi’s Island (SuperFX2) and pseudo hi-res Kirby’s Dreamland 3 (SA-1 - at certain stages it might drop a few fps) should run at fullspeed on a Celeron 733-class CPU (Xbox 1) - and on Wii (which is a bit faster than the Xbox 1) even Yoshi’s Island runs at fullspeed.
1080p might simply be out of reach on your particular system. If things run fine on 720p I would suggest sticking to that - you might get more input lag though if this isn’t your HDTV’s native resolution.