That's the "only possible difference"? Really? There aren't any other possible differences?
Do they both operate under the same government regulations?
Are your deposits insured in both by the Federal Deposit Insurance Corporation (or some other equivalent insurance underwriter)?
Are they both held to the same financial audits?
Not every country has deposit insurance or serious audits, and also, deposit insurance schemes has limits. And in some cases, I think deposit insurance isn't sufficient if a too big bank fails.
Criticism often comes to online wallet providers (Xapo, Coinbase, etc) saying, if you don't own your private keys, you don't actually own your bitcoin. On the other hand, if your cash is in a traditional bank, you don't really own your cash either. The only possible difference, traditional banks have been around longer, and more people trust them. Many bitcoin users who criticize bitcoin vaults, store their cash in a traditional bank. Hypothetically, if Bank of America, or Barclay, or DeustcheBank announced they've invested millions into a highly protected, advanced, security architecture, would you trust someone to store it then? I personally don't trust myself to store my own bitcoin, for now. That could change in the future, but right now, I'm not a fan of the options, as the technology depends too much on my ability to maintain hardware, or, not lose something. I think about pictures, movies, files, documents, I had on my computer 10 years ago (and I always backed up), and I probably couldn't retrieve a single one without relying on a cloud-based service (Facebook, Google Drive, Dropbox, etc.). I have no idea where the original photos of my trip to Indonesia in 2008 are, but I know that album is still easily accessible on Facebook. Are critics right to say, don't use an online wallet provider, it's not safe?
This is true, but securing physical cash in some places of the world is really hard. I can't go to the street (in my case, a big city in Brazil) with an amount equivalent to 1 BTC without suffering a serious risk of being robbed with a fire gun, by the way, a lot of assaults here occurs just after you go to the bank and withdraw some cash (known here as "saidinha bancária", or "bank exit"). In these last 2 days I also exchanged some US dollars which I had at my home for Brazilian Reals, but immediatelly after exchanging it, I deposited the reals at my bank account, because:
1. I didn't want to take the risk of being back to home after exchanging money, even doing this through a legal exchange.
2. With the devaluation of Brazilian Real against the US dollar (now it's 3.29 BRL per USD, against 2.32 BRL per USD one year ago), the excess of banknotes was damaging my wallet and eventually could lead the attention of other people.
Personally I don't trust in my bank at all, specially because I don't trust in fractional reserves, but I think in mycase is just the lack of other alternatives. Also, a lot of people and business still use banks for payments, so I still need a bank account to receive these payments.
OTOH, the idea behind Bitcoin is to bring to you the control of your money, specially on its eletronic form. So, if you go to a Bitcoin bank, you bring to the bank the control of your money, in the same as it happens at fiat money. So, why Bitcoin?