Well, switching from a 12-27 to an 11-28 isn't going to be much of an improvement for hill climbing purposes. So, that more or less leaves you with mountain gearing. I, personally, would opt for the 32, but that's because I currently hate the wide jumps I have to deal with on the flats with my own compact road set up. If that's not an issue for you, then go with a 34 or 36.

I'm no expert on road/mountian compatibility. Is your current group Shimano? Just make sure that whatever mountain set up you get is compatible with your road shifters. I vaguely remember reading that 10-speed Shimano road shifters are (or at least once were) only compatible with a 9-speed mountain cassette. I think SRAM also offers an Apex 12-32 10-speed road cassette that would be compatible with a Shimano 10-speed drivetrain--if that's what you have.