Basically, as the title suggests, which expansion is harder to beat?

I'd say SI, but I had no real troubles with either.

Shivering Isles is the only Expansion. KotN is downloadable content.

KotN provides a very lengthy and involved questline with multiple quests and backstory.

Shivering Isles provides a whole new land to explore, a main questline, and a bunch of side quests and lots of NPCs and items.

As far has "harder" if you compare the KotN questline to Shivering Isles, they are about the same I think. There could be an argument that the KotN questline is a little more difficult but not much. Both are fun. But again there's lots more content to Shivering Isles.

both were easy. however, I will add one caveat: the KotN quest was slightly annoying, because some of the wayshrines were ridiculously off from the map.

Yes I agree completely the wayshrines are so annoying!!
Anyway, both include a final boss that is difficult enough. What I like about SI is you can fight huge groups of decent enemies at many points in the main quest. There were several times on my best character when I would fight 10+ knights at once. I love the shivering isles main quest line and landscape. I have to say SI is harder if you pick hard fights, and is all around better

I would say that SI is harder but only because it's longer and it's a whole new land with loads of new items and ingredients and such.
So my response, SI.
KotN is also great, however

Shivering Isles, just because some of the new dungeon traps it introduces are quite nasty, and shutting down obelisks can be hard work if you don't know what you're dong.