For the most part I would have put the GBA (and DS because it fed from it) debug efforts/options at just behind FCEUX (them lacking some of the fun stuff like new executed routine elimination/noting, though you could usually do it manually) and considerably ahead of just about everything else. I will give though that I have not played with the debug SNES emu you mentioned enough to be comfortable with it and not read menus all the time. To that end I don't know if it is a lack of functionality, missed the function on the menu or a difference in workflow. I will say though it is quite doable to start by looking at something in the VRAM, reverting to an earlier state and even if it is one of those weird games that does not DMA, BIOS call (more on that later) or CPU copy data straight from the ROM (all of which is directly mapped in memory for all commercial games anybody cares about) into VRAM and instead will send it to WRAM, do some operations on it and then kick it to VRAM still find yourself looking at a memory grab from the ROM a few minutes later to in turn point your hex editor/tile viewer/whatever at it, or watch functions to determine how they work to in turn write the equivalent of https://www.dragonflycave.com/mechanics/gen-i-capturing
But yeah the two main debug emulators for most are whatever version of VBA works for them (I have not properly done much with VBA-M of late and its inclusion of debug tools was somewhat lacking* back when, or maybe just being kicked to GDB) and no$gba debug, which on the other hand is great. Some might combo up emulators to gain info to feed to others.
*in case you were unfamiliar then VBA was the major emulator during the GBA lifetime, the GBA being emulated pretty well from day -1 really (its SDK leaked ahead of launch) and pretty good indeed by the point of the NA release. Some years later its author quit and his successors did not do all that much, and by that point there were also a hundred different active forks (linking support which vanilla VBA stated they would not do, link with real GBA, enhanced cheats, couple of debug ones, "smooth", accurate/superior audio, the TAS world had a couple, some for fast computers as this was still the point where you might expect some not to have SSE/SSE2 in their CPU, some bug fix ones, one for more accuracy, one for homebrew debugging, some for better recording options and it goes on for a while). VBA-m then being the project that attempted to merge, or at least take the best bits of, the lot which stuck (there were a few others attempting to merge a few).https://vba-m.com/
and I quite often link https://www.romhacking.net/documents/361/
as an example in general for tracing for all systems even if it for an older command line based VBA fork (vba-sdl-h manual http://web.archive.org/web/20130215155212/http://labmaster.bios.net.nz/vba-sdl-h/
is good stuff and its hardware documentation** is some of the best on the GBA http://problemkaputt.de/gbatek.htmhttps://mgba.io/tag/debugging/
is more about quirks and oddities in emulation but good reading. The Shrek videos thing is also the only exception to the everything is 32 megs or less, homebrew can vary a bit here (flashcarts, the PCE-CD emulation and pogoshell) but also mostly sticks or can be made to stick to the 32 meg limit.
Not sure what Higan has nowadays for hardcore debugging options but I generally got annoyed at Higan's use and debugging elsewhere did for me.
**the main listhttp://problemkaputt.de/gbatek.htmhttps://www.cs.rit.edu/~tjh8300/CowBite/CowBiteSpec.htmhttp://www.coranac.com/tonc/text/asm.htmhttps://blog.quirk.es/2008/12/things-you-never-wanted-to-know-about.htmlhttps://patater.com/gbaguy/gbaasm.htm
is very outdated but might as well have something.http://belogic.com/gba/
is for the audio but there are none better, navigation at the top of the page. If you are interested in audio the vast majority of GBA games (though not as great a majority as the SDAT format on the DS) will use the "sappy" sound format for which you can find many tools and documents on this very site.
Back on topic
Watchpoints are a thing for most of the emulators. Breakpoints too, all the usual suspects save maybe run to line (though you could probably just do a break on execute)
When you say debug logs though most will think you want the BIOS SWI compression call logs as that is what most do. There are even compression tools that will read VBA's output here.
I don't know offhand if the SNES stuff does some kind of self documenting/pipe all output and entered commands to a text file that you pore over after the fact and that is what you are missing but some logs should still be a thing, and for the most part I just note things separately anyway.