I am going to respond even though the OP already decided.
I don't think C-1 is harder than Tenergy 05fx. C-1 has a soft top sheet. They are about the same to me, except T05fx is definitely more bouncier and less controlled than C-1. C-1 is like the Jack of all trades.
I agree with
@Der_Echte, you just need to try them and see which one you like the most.
I used to use G-1 on the backhand side when I went with 5-ply all wood.
Then when I tried outer carbon blade, G-1 felt weird or too fast on my BH side, so I switched to C-1 and I was very happy with it.
About 1.5 months ago, I started experimenting with inner carbon blades so I went back to harder rubbers. When I started playing with inner carbon blades, I just realized that softer ESN rubber was not pairing well with it.
I just did the test earlier this week: three blades, identical, all have hurricane on the FH side. BH, I put on Dignics 64, Tenergy 80 and Stiga Mantra Pro H. All max sponge. Guess how I liked them? I liked Tenergy 80 the most, Stiga Mantra Pro H in the middle and Dignics 64 the least.
Why? I have no idea. I just put them on and my hand told me what I like and what I don't like. You would think that Dignics 64 being the most expensive and should be the best. But I felt that Dignics was a bit dead. Tenergy 80 seems to hit the sweet spot in terms of hardness and ability to grip the ball. Signa Mantra Pro H, honestly, I got that sheet from Dandoy a year ago when it was on sales. It is 50 degree hardness. I just threw it on because I have it lying around. And surprisingly it felt quite good!!! But yet Dignics 64 felt a bit dead). Go figure.....
At the end of the day, not everyone can afford to try many different equipment and find the combination they like.
But as
@Der_Echte said, there are many rubbers that behave the same. For example, C-1, Rakza 7 soft, Acuda S2, M2, EL-P, Barracuda, Rozena all felt about the same and my hand could adapt to all of them (except Rozena felt slightly harder than the other rubbers so I need a bit more adjustment) when I was playing outer carbon. They were all very good.
Now that I know I like harder rubber on the backhand on inner carbon blades, I kind of know what types of rubber should be "good enough" to test in the future.