I'd say Heartbleed was worse. This one requires local code execution, whereas Heartbleed was "connect to any OpenSSL-using server, send a magic packet, and read the private keys from its memory."
… and nowadays almost everyone permits remote sites to execute code in their browsers. I don't know if JavaScript can be used to implement Meltdown though.
This research has implications for products and services that execute externally supplied code, including Chrome and other browsers with support for JavaScript and WebAssembly.
Edit: Wait, sorry, I misread. Read is all you really need, write would just be a cherry. If you can read the memory of the host kernel, then you can gain access to any other VMs on the system. This one is bottom-up, you need access to one system and in theory you can gain access to thousands.