Both are similar in terms of location. They are quite close to each other. The IC is a little more convenient for the metro (which takes you to the airport), the HR a little closer to a tram line.

I think Sofia is pretty much walkable from both locations. But I'm European and as such perhaps don't mind walking as much (I assume you're hailing from the US). Otherwise, public transportation is dirt-cheap, a single ride costs like BGN 1.60 (which is around $1) and a day pass is BGN 4.00. Taxi is not unreasonably priced, either. But I don't speak Bulgarian and would be at least somewhat worried about being taken on the scenic route.

The best-located of the upscale chain hotels is probably the Luxury Collection. I never stayed there. You'll most likely pass by it when exporing the city, though.