I have to be honest, if you like the T05 and not the MXP, I am not sure there is much you would like. But, a question:
MXP is harder than T05.
Harder rubbers are harder to use on BH.
Usually, someone who knows what they are doing has the same rubber on FH and BH or the softer rubber is usually on the BH.
This is because the FH stroke is so much bigger and so much easier to put the body behind it that almost all players have more impact on FH than BH which means the harder rubber gives more for FH. Softer rubber actually gives more for BH.
Why not flip the racket and use the MXP on FH and T05 on BH or make it so you have T05 on both sides.
Most players who decide to get different rubbers for FH and BH do it without knowing what would be useful for each wing and why they are getting different rubbers.
If you are in that category, you would be better off with the same rubber on both sides. Having rubbers as different as MXP and T05 without knowing why you are using one on FH and the other on BH can actually cause one wing to improve slower than the other. In this scenario, the wing with the harder rubber that should have the softer rubber is the wing that would suffer. MXP could make your BH improvement happen much more slowly or could even block the improvement.
On the other hand, sometimes there are players who are decently high level and know exactly what each separate wing needs. That is a different issue.
But most players who have very different rubbers on FH and BH without knowing why beyond, "in an online review, so-and-so said MXP was a good BH rubber, and so-and-so said T05 is a good FH rubber" can really slow their own progress by the EJing that causes you to tinker that way without having an understanding of what each wing actually needs.
There is really no such thing as an FH rubber or a BH rubber. There are always a range of rubbers that will be good for a particular player. But if the FH and BH rubbers are significantly different and there is no well thought out reason why, usually that kind of thing is detrimental to a player's improvement.
The notable exception is H3 or other tacky rubbers like it. If you are using that on FH and developing the FH technique that goes with it, you would definitely want to choose something way way softer for BH like H3-60 or T05, or T05fx or FXP.
But when you do that, the FH and BH strokes will not develop in a parallel way and you would just need to accept that.
It is also worth looking at top pros who use tensor type rubbers: So many of them use the same rubber for FH and BH. Like Timo Boll uses T05 on both sides. There is a reason why these guys don't use T05 on FH and Andro Rasanter 45 on BH. There is a reason they are not using completely different rubbers on FH and BH.
Anyway, I hope that information is useful.