I don't personally believe that Litecoin will grow to as big as Bitcoin, but it's way too early to speculate on this in my opinion. Bitcoin was first introduced in 2009, that's 4 years ago. Litecoin came out in 2011, two years later.
I don't believe it will either. But it brings up an interesting point. With all of the other ALT currencies and LTC being called the Mastercard, what is Feathercoin? Novacoin? I believe that at some point there will be an established 2 or 3 coins. Bitcoin is the #1, will LTC be next? It will be very interesting to see where we are at this time next year. By they we should have a good idea of market cap, public usage/awareness and acceptability.