As a leading web wallet I don't think that blockchain wallet has some competition, at least I'm not aware of it.
They got the best domain for making web wallet as bitcoin is tied up and well known to its blockchain technology. Every newbie will recognize "blockchain" and will trust to them since they got the domain.
However, web wallets are the least secure and I suggest that you avoid that option or at least combine it with some other types of wallets.
Don't store too much bitcoin there so that you'll be at least safe, don't trust web wallets that much.
So you could choose among Electrum, Mycelium or Ledger as my favorite wallets that I can strongly recommend.
I'll go with Electrum if no budget of buying a Ledger nano S, also greenaddress is also a good wallet.