I had the H8-80 38deg on backhand before. As it is bouncy, it also can be really dead in the flat hits. I really liked it in the blocking/defending game, but it demanded a bit too much of my technique on the offensive part to work allright. I've used a Yinhe V14 Pro blade for testing..
Actually my son used Dignics 05 on backhand, and as it is super expensive we've tried to find a replacement for this one. He has really great backhand technique and uses very much of the D05 potential, so it has been hard to find something else. But now, for three months back, he's playing with Joola Ryhzen AGR that gives him the spin of D05 but lacks a little bit in speed compared to D05. In return he gets much more control in the short game and flat hits, so for now it looks good.
Back to the H8-80 37deg vs H3 37deg compare. I've tried the H3 37deg as well for backhand. It's a huge difference compared to the H8-80. The sponge isn't soft enough to give you the security for a backhand rubber and the spin/kick H3 gives you when hitting right isn't there. I assume that the softer sponge doesn't quite go with the stiffer top sheet of H3? Anyway. This was not for me.
I use Yinhe Big Dipper 38deg for backhand, and it gives me more "what-I-want" in a backhand rubber. It's more responsive than H8-80 and it's kind of a "do-it-all" rubber that shines in the spin/control area. My son (mentioned above) played for a month or so with the Big Dipper 39deg (BH) but it lacked some power he got from D05 that we compared with then. I feel, when hitting right BD 39deg is superb for the money and BD 38deg is more forgiving and safe.
A tacky, more bouncy rubber than BD 38deg is Giant Dragon - TopEnergy Soft. I've also tried the new 729 - Dragon F Medium Hard. This is also in this backhand rubber area, with it's softer sponge and tacky top sheet. It gives a bit higher throw than the others I mentioned, so if you like that it could be something for you.