I've had quiet a few crates and panicky dogs, so I'll share my 2 cents. Wire crates have their pros and cons. A dog who is determined to escape if it means chewing a leg off has a higher chance of hurting himself, simply because wire does bend if you put enough pressure on it. That being said, I have never had a dog actually bend the door enough to escape, and three have really tried! Usually the latch will wiggle loose before the crate gives, and they escape by bending the loose half of the door open. If you clip some D-rings on the latch, then no dog can escape. Another bonus: they are collapsible, so you can put them away in storage when you don't need them.
Not all wire crates are created equal. Top Paw makes some of the sturdiest ones.
The plastic crates have a lower chance of causing injury to a neurotic animal. That being said, the solid wall can intimidate dogs who are not used to being crated. It takes a little more time and training to get one to enter, and a truly terrified dog will never go in on his own, and probably bite you in the process. With a wire crate, you can at least thread the leash through the wires at the back end and gently "lead" him in that way. I've had a lot more success in that area with the wire crates.
I personally own both styles. I use them for different dogs depending on their needs and personality. Headstrong dogs go in the wire crates every time. I can get them in/out easier, they sometimes settle down better in them, and as long as I add a clip to the latches, I've not had one escape. The only "bent open and escaped" situation happened when I did not secure both latches.
I would say it's very uncommon for a dog to escape from a crate, even in the crazy situations where the dogs injures himself in the doing. I've only had it happen once in a history of over 30 dogs so far, and it was that dog who taught me that those latches really do wiggle loose if you lick them and nibble at them for long enough.
Long story short: definitely get a crate to keep everyone safe at night and when you are not at home. Go online, read product reviews, and make a decision that is best for you, your situation, and your preferences.
Thank you so much for all the info everyone! I ended up having two crates brought by two owners and they were helpful at feeding time. Other than that, they always stayed open but one dog enjoyed going in there for quiet naps and another crate-less dog even used one for a couple of naps too.