Partitioning Vs. Split Databases - performance?

I'm breaking up a database into several sets of data with similar layout. (we
currently have multiple customers using a single database and tableset, we're
splitting it out to give us more "wiggle room")

It seems that there are basically two ways to proceed:

1) Copy out the data specific to a customer and load into a separate database
for that customer, or

2) Copy out the data specific to a customer and load into separate tables
(with slightly different names, EG table "dates" becomes "cust1_dates") and
use data partitioning to help with performance as needed.

Given the same physical hardware, which one is likely to perform better? Does
it make any difference? Does using separate databases use more RAM than a
single database with a bunch of different tables?

Company is growing rapidly, so growth room is important...

-Ben
--
"The best way to predict the future is to invent it."
- XEROX PARC slogan, circa 1978