> "H" not clearly discernable in the two green blobs, no reference to medicine at all

I've never seen either of these logos before, but in the new one I immediately see the "H" formed by the white space between the two "green blobs", which to me look like "healing hands" and which I take as a medical reference (although TBH they do make me think "chiropractor" rather than "doctor"). I don't think the new one is great, but I much prefer it to the old one, which looks like a very half-assed attempt to combine an H with the Rod of Asclepius. It's like they weren't even trying.

What I meant to say is that the old one is a logo that (without any text or anything) practically screams "hospital"/"medical institution" to anyone looking at it for the first time, while the new one is rather ambiguous, especially if you have no context for it.