Of course, bitcoin startups really want to use the second model, where THEY control the money, which gives them many more avenues for profit: As any salesman knows, the closer you are to the money in a business, the more money you're likely to make yourself.
This means bitcoin companies are bending over backwards to say "look how safe your money is!" However, be aware if you ever buy bitcoins, it is much better to store your own bitcoins or use a wallet that allows you to manage your own private keys, or use a (now trendy) multisig wallet where the wallet company can't move money without your permission.
If a bitcoin bank says "We insure our bitcoins" your best response is "No thanks, I'd rather not have to trust you with my money in the first place." The whole raison d'être of bitcoin is that such trust isn't necessary.