HIBP is a great service and was the first one on the scene. HEROIC has more breached records than HIBP and with a free account on HEROIC you can see more details about how you have been compromised along with better search capabilities.
But apparently not a strict superset of HIBP, since your site shows nothing for an address that I know was exposed in multiple hacks/leaks.
We should have everything that HIBP has plus another .5 billion.
HIBP is still useful to me, at least, because it will let me find breaches for my entire domain, rather than just for specific email addresses. This is useful since I use a different email address per-site (username-somestring@domain), so just being able to search on my base email address on HEROIC isn't likely to turn much up...