Running multiple databases on one database server potentially reduces memory requires assuming the databases are using the same page size, you will leverage common memory and the server instance for the databases. When using databases with different page sizes the memory in the database is cache is not optimized as there are empty cache pages which is not optimal.
The database server will take advantage of multi-processor machines.
When running multiple servers you are effectively running with two caches and server instances which of course take up more memory. If your databases have different pages sizes, running two servers may actually benefit you as you can set up a database server for each page size and optimize cache memory.
Having dataabase and logs on different devices will also improve performance as it can reduce IO contention.
My comment on multiple page sizes on a server stems from the following:
If you are using a database on a server with a page size of 2K when the server is running at a 4K page size, each of the pages in the cache for that database are wasting 2k (4K -2K). This is less than optimal of course. Switching to different pages sizes should be evaluated on an application by application basis and the answer will depend on your environment. Going to very large page sizes usually is not warranted as most applications are served well by pages size 2K or 4K.
If memory on the machine is not a concern, then performance should not suffer too much unless one database server is overwhelmed and the operating system does not give any cycles to the other server( the operating system likely will not do this however). There will also be more task swapping between database servers which can be an expensive operation.