With Handshake, certs can be pinned directly on the blockchain, which becomes more secure as more nodes join the network and across time as more blocks get mined on top of the pinned cert. This shifts the system from diminishing security to accumulating security. That’s the main innovation behind Handshake.
There are other differences in the issuance model as well. Namecoin’s issuance destined it for failure from day one since names are registered for a flat fee without restriction. This meant that squatters and early adopters could lock up the namespace without paying the true market price of the name. Handshake uses an auction system for name registration and releases the namespace over time (the release date is determined by hashing the name % 52), which means that names are registered for their true market price and newcomers can still register good names. This difference is critical and already playing out successfully — the highest auction was for 200k HNS, which is equivalent to $20k USD and 7/12 of the namespace is still unreleased.