I like both for different reasons.
The house we are currently in had 2 wood-burning fireplaces when we bought it. Upon having the chimney cleaned, he informed us that there was evidence of past chimney fires because they weren't properly built/pitched and advised us to not burn wood in them anymore. So we converted both of them to non-vented natural gas fireplaces. The irony here is that we also have cleared about 50 trees from the property (don't worry, there's still a bajillion left) since we bought it in 2012 and had to give away and sell all that good free firewood (we can use some for the fire pit, at least). I had been looking forward to listening to the crackle of the fire in our living room, but unless we wanted to remove and rebuild the chimney (not happening for the foreseeable future), it was unfortunately not to be.
We went with non-vented to keep more heat in the house. They definitely do the job, the living room can get quite warm very fast. We have cold winters in Buffalo. I do enjoy not having to drag firewood in from outside during winter, make sure enough wood is split, vacuum up dropped wood crud on the way in, and no chimney maintenance. It also has a remote control. I'm thinking about upgrading to the remote that has the built-in thermostat. I have 3 zone heat in my home and many evenings in the winter I can shut off the living area zone and just run the fireplace instead. It can add some humidity into the house, but our winters are so bone dry that doesn't affect anything. Vented gas fireplaces will lose a lot more heat.
Ultimately I wish we were able to do something like make one of the fireplaces gas and the other wood, but not meant to be. My parents have both -- actually they have 2 wood-burning fireplaces and 2 propane fireplaces (their house is substantially larger than mine). They use both, but for different purposes. If they want to just sit in front of the fire and read a book with some wine, they will choose to sit in the library with the wood burner. If they want to watch a movie and aren't staring at the fire/listening to it, then they sit in the family room and use the propane one.