I've found that speaking with the captain and crew as well as watching them carefully gives me a good sense of how they approach things. However, you never know what will happen which is why the two most important things are relying on yourself and having safety devices correct for your situation (e.g., Nautilus Lifeline/PLB, safety sausage, etc.).
Case in point: I went out with a boat and crew in the Bahamas I felt very comfortable with...I'd been diving with them multiple times over a few years. Then on one dive (my best friend's open water cert), a DM asked the captain to switch with him as he was feeling tired and cold. At the time, I thought this was a little odd, but then thought, ok, they really are serious about being safe. I thought this until we surfaced to find the boat had disappeared.
We had 2 DMs for two groups of six and an instructor for my friend so I wasn't that worried since it was 15 of us including crew...people will obviously be able to find us and will know we're gone. I became worried when they told us to drop our weights around the 30 min mark. One guy then says he has a Nautilus, but that he left it on the boat since he felt it was such an easy location. (Thanks, guy!) At the one hour mark, the waves started getting really big as a storm rolled in much more quickly than expected. By the 1.5 hr mark, I started to wonder if we should attempt to make land...but it was so far away. Then we finally see the boat, but with the large waves, the boat can't see us even with the safety sausages/mirrors/etc. Finally, an hour and 45 min later, we're found. I felt so bad for my friend since it was her 2nd open water dive, but she was surprised. She thought that because we were all so calm that this kind of stuff happened all the time. (!)
So what happened? Stupid DM fell asleep on the boat. Mooring snapped. When the DM woke up, he didn't want to get in trouble so he decided to try and find us on his own, but somehow couldn't. When he enlisted help, we were on board the rescue boat within 20 min. The DM was of course fired on the spot.
Lesson learned: Even if it's a great outfit, one stupid person can really put your life at risk. I bought the Nautilus Lifeline before my next dive trip and don't go on any dives without it.