Any issues with higher power springs?

It depends on how much stronger the spring is. I tried some stupid strong springs in my D56 and I had a very difficult time cocking the rifle till I got down to a wire diameter of .135. Remember, you can't really increase the power of a springer all that much more than it is engineered to be by the manufacturer. Its easier to get a very powerful airgun and then tune it down.
 
They tend to get harder to shoot as accurately and often becomes hold sensitive.

This. I had a very difficult time learning to shoot my asp at 21FPE at the muzzle. I figured being a gas ram would maje it easier, but boy was I wrong. The learning curve was steep I suspect as a result of the power. Didn't have the same issues with my other, less powerful, guns...