You can use both.
"Than" is a conjunction used in comparisons:
Tom is smarter than Bill.
This is more important than you might think.
Is she taller than you?
Yes, she is taller than I.
Better than= To a greater extent or degree
Technically, you should use the subject pronoun after than (e.g., I), as opposed to the object pronoun (me). However, English speakers commonly use the object pronoun.