Decision criteria on when to use a non-dbo schema vs a new Database
I'll start by saying don't consider schemas as namespaces or object domains in the OO sense. Schemas are essentially permission containers with some added value (see below)

Also, "separate schemas" or "separate databases" are 2 different concepts. Data that needs to be transactionally and referentially consistent needs to be in the same database.  See One Database or Ten? blog article for more.

In that database, you may or may not use schemas for organising your objects.

Personally, I'm a fan of schemas and always use them but for things like permissions and logical grouping. For that, I'll refer you to previous questions where you can see the general opinion is in favour of them:


Schema design - best practices?
What standard should I follow when naming tables and views?
Over use/correct use of schemas?


For the case for separate databases, see Aaron's answer, but this all hinge on the "transactionally and referentially consistent" requirement.