I think you are right bitcoin do not have any competitors, as bitcoin is a bigger crypto currency and most people want to put their money in bitcoin and are using it as a currency while other coins are only used for trade,
The Etheruem is the competition of the bitcoin. The market cap of Ethereum is about 10% of bitcoin. It will get bigger.
Yes, you are right, Ethereum's market cap is $940,376,672 which is impressive and it will get bigger in the future most likely, but Bitcoin's market cap is $9,111,309,781 and there are no reasons to think that it will be growing slower than for Ethereum.