Join tables in two databases make query slow? is better to partition db?
You've got a bunch of different questions in here, so let's break 'em out individually.

Q: If I join two tables in the same database with the above query, why is it slow?

A: For starters, you're not using a WHERE clause, so SQL Server has to build the complete result set, merging both tables together. If you only need a subset of the data, consider using a WHERE clause to just get the data you need.

Once you've done that, note that you're using a LEFT OUTER JOIN. This tells SQL Server, "Not all of the table1 records will have matching records in table2." That's totally fine if it's true - but if you know all t1 records will have at least one t2 record, use an INNER JOIN instead.

Next, indexing starts to come into play - depending on the width of the tables and the numbers of fields, you may want to add indexes on the fields you're using for the join. To get good advice on that, it's best to post the actual execution plan you're working with.

Q: If I the tables are in different databases on the same SQL Server, does that change anything?

A: No. There's some interesting gotchas around things like default isolation levels in different databases, but for the most part, your queries should produce the same execution plans and speeds.

Q: Should I use table partitioning to make this go faster?

A: You mentioned database partitioning, but there's no such thing in SQL Server - I'm guessing you meant table partitioning. Generally speaking, no, I wouldn't jump to database design changes in order to make a join go faster. Start with the basics - understanding SQL Server execution plans - and only make database design changes to solve problems that you can't fix with things like indexes.