Karakol is the established base — more infrastructure, more tour options, easier logistics for a first trip. Jyrgalan, 60km east, is the newer, quieter alternative that's grown fast around community-run trekking and, in winter, backcountry ski touring.
If this is your first trip to the region and you want options (horseback, yurt stays, paragliding, easy day trips), stay based in Karakol. If you're specifically after trekking with fewer other visitors on the trail, or you're coming in winter for ski touring, Jyrgalan is worth the extra hour and a half — it was literally built around exactly that.
You don't have to choose one or the other — a Jyrgalan day trip from Karakol is an easy way to see both without relocating.
Zoomy