I've been primarily using heavy armor as a spellsword kind of character, and am curious just how differently my experience might be if I were focused on light armor instead. I've read that it offers higher mobility, but is it really that noticeable? Anyone played a lot with both types and developed a preference, and if so why?

There is a difference, I was using heavy armor one time and I was on a quest with an NPC who had light armor, I kept on having to sprint to keep up with her.

Isn't there a perk for heavy armor that reduces the movement and weight penalty for wearing it

im 50 % magic 50 % sword with heavy armour it works good since you can take a beating

if you are light armour and not a assassin or a magic dude YOUR Screwed

I've been wondering about this myself. I've been going pure warrior with 2H weapons and I have been trying to decide between light armor and heavy armor. I really don't know... I like the armor of heavy but I read there are some good perks with light armor. Still can't decide.

No.
I'm not, actually.

My main character is wearing Light armour, using a war axe and bow. He's living off the land (off the grid) and having a hoot!
Hit-n-run tactics are working quite nicely, thank you very much.
He chooses his scraps rather than letting the scrappers choose him.

I think it may effect weapon speed as well, but not 100% sure.