Smart Phone vs Online Wallet/Vault Is a smart phone wallet (i.e. Mycelium) safer than leaving BTC on an online exchange like Coinbase?
It is safer from some things, but not others.

For instance, let's say you don't have your Mycelium seed backed up (which you should do), and you drop your phone in the toilet.  This could cause a loss of funds, if your phone no longer functions.  You won't have this problem with Coinbase.  Someone could also stop you at gunpoint on the street, and demand you transfer your phone's bitcoin to them.  If you don't have access to your Coinbase funds from your phone, this type of robbery won't work.

On the other hand, Coinbase can freeze the money you store with them (both fiat and bitcoin) for basically any reason.  This would usually be at the request of a government or another financial institution.  When an online service holds your bitcoin, it's best to think of it at their bitcoin, and you just have an agreement to be able to spend it.  That agreement can change, and there's not much you can do about it.

Different types of wallets mitigate different risks, and in different ways.  It's not as simple as one being "safer" than the other.  I wrote about this a lot more in a different answer, if you care to read it.