I tend to use different rubbers on FH & BH, different manufacturers as well as sponge hardness / and sometimes thickness. although usually the difference is with sponge hardness rather than sponge thickness.
My profile shows Donic Bluestorm (DSS) Z2 FH and Z3 on BH both in max. Z2 is 47 degree, Z3 42 Degree, this is a fairly big hardness difference, usually many prefer or recommend a 2 to 3 degree difference in sponge hardness, but in reality its horses for courses and what suits you better!!!
Some players may have an exceptionally strong BH and prefer a harder sponge on that wing compared to their FH wing!!!
DSS Z1 and Z2 both have 47 degree sponges but the difference is with the pimple structure!!!! which changes the rubber characteristics slightly!!!! so even more to think about!!!
Some say that rubbers with thinner sponges are slower or easier to control and generally that may be the case, but when you think about it, with harder power shots a softer thinner sponge will mean that the blade is more easily engaged, if its a fast blade, then it may be the case that a thinner soft sponge rubber could actually play faster!!!
The general the idea behind using a slightly softer rubber on the BH is to assist with speed/power and to a certain extent control (control is always in the hands of the player!!! some rubbers are easier to control, but they DON'T actually have control themselves!!!!!) its easier to produce power on the FH side, a softer bouncier rubber on the BH helps with speed, and possibly a thinner sponge does as well (under certain circumstances).
Is the difference really that noticeable between 1.9 and 2.1mm sponges?? or 2.1 and max?? for some yes and others possibly not !!!!
I used to use the thinner sponges on both FH and BH ( when using bouncy sponge / grippy top sheet rubbers, but now would go for max thickness ) and max (or in the case of a boosted H3 2.15mm to allow for booster thickness [in case I wanted to boost] ) for tacky hard sponge rubbers, but would still try and choose a softer sponge version on BH side, especially now DHS have made the 37 degree versions more widely available (BH)
Currently I have Rakza Z max on BH and Rakza Z max extra hard on FH (haven't altered profile yet!!!!) Playing well with this combo, would I play well with the same rubber s on FH and BH, probably!!!!! its actually pretty hard to tell how much difference the different sponge hardness actually make !!!!