You might need to do both, and it depends on your ideal customer's buying patterns. If that buyer typically purchases your product and your competitor's product in a single transaction, and that buying pattern makes sense, you gotta to build, buy, or partner to offer your competitor's product. If you don't, you could quickly get shut out of the market altogether.

Partnerships are messy, but they're so fun. It's good to have friends in the market, and making the choice to partner can really clarify your company's purpose: the problem you want to be known for solving better than anyone.

Last thought: when you do pick a truly new problem to invest in solving, just make sure it's one you and your team care deeply about. You only got so much time to play with--do you really want to use it building a better mousetrap?