Well, i play guitar too, so i know that the same principle applies here. Only press as hard as you need to. There's no need to grip the neck very tightly even while doing barre chords. If you need to press really hard to do barre chords, one or more of these things could be wrong.
1. Your action is too high - the solution is easy, get your action lowered
2. Your technique is not good - work on your technique. Sometimes there's a string or two that doesnt get pressed down. the solution usually isnt pressing harder, it's changing the shape of your hand. Try it.
3. Your calluses aren't developed enough. - some chords can be hard to do (or mroe painful to do) without good calluses since calluses allow you to play more easily. All you can do about that is practice more
There's probably more, but i hope this helps. You shouldn't ever have to press very hard or grip the neck tightly...unless you like doing it...
