I can't vouch for BitMarket.eu but relatively speaking I have not hear of them lying, stealing or being hacked or any combination thereof so that puts them at the head of the pack for most prominent bitcoin exchanges
I've used them for all my BTC purchases except the very first. The difference between them and exchanges are that they're only brokering
1 the trades - the buyer pays directly to the seller. They do escrow though, which means they could in theory do something funny once the BTC are released by the seller into your account. So far, as you state, I've heard of no such issues. I also like that there are no day traders, too small volume and there's a general price premium
2 above the popular exchanges.
I alway withdraw immediately though, there's simply no point in not doing it. I think it's good advice.
(There's also some basic persona verification being done when registering)
12) That's also why I wouldn't consider them to be a "competitor" to you.