Probably not in the next 10 years. Ethereum took 2 years to come out ,and its just a pile of crap, with all the hacks and scams going on there. (not to mention the hardforks).
Best candidates would be:
LTC = Which is a copycat, so probably not
NMC = Which doesnt really serve as currency
MONERO = Probably high chance, but it doesnt even have a GUI wallet yet, so better make that come out first.
Other than that, there is no viable competitor to bitcoin ,and probably wont be for the next 2 years, and to beat bitcoin...? That would take a lot more than that!
i would like to nominate litecoin instead any other cryptocurrency ,
they have a very strong community and did not often lost too much value ,
even you must realize that the chance this thing to happened very low ,
bitcoin are too big to be replaced.
The Monero is too different from the bitcoin. It uses totally different technology. Its blocks are bloating fast.