In terms of being able to send/receive bitcoins? Nothing

In terms of security... a LOT. A good hardware wallet provides and extra layer of security by effectively "air-gapping" your seed/private keys from the world... even if it is connected to an internet enabled device.

A software wallet on an internet enabled device does not. Malware or someone with remote access can copy your wallet file, keylog your passwords etc. With a hardware wallet, they cannot... because the only thing the HW wallet does is receive unsigned transactions, and output signed transactions. The private keys are not accessible (even by malware)... at least, that is theory!