Briefly, ICAP addresses are safer to use, since they have a checksum which provides protection against mistyping an address. But ICAP adoption isn't as widespread currently. For mining you can use either, since a HEX address, when needed, can always be obtained from an ICAP address.

More information:

What is an ICAP address?

Why don't Ethereum addresses have checksums?

See also questions tagged with address and icap.

Briefly, ICAP addresses are safer to use, since they have a checksum which provides protection against mistyping an address. But ICAP adoption isn't as widespread currently. For mining you can use either, since a HEX address, when needed, can always be obtained from an ICAP address.

More information:

What is an ICAP address?

Why don't Ethereum addresses have checksums?

See also questions tagged with address and icap.