I think it could go either way, but my money is on Litecoin.
Bitcoin is the original cryptocurrency, and it has a big head start over Litecoin. But I think its popularity has also made it more susceptible to attack by hackers and other criminals.
Litecoin, on the other hand, was designed specifically to be more lightweight and faster than Bitcoin. So I think it's likely to become more popular in the near future as people come to appreciate its advantages over Bitcoin.