Mister. Mister still provides an option for your chameleon to drink droplets of water gathered on the leafs and what not. Also, foggers with my experience for reptiles can really over due the humidity in a cage which could lead to respitory problems. So my opinion. Mister. I have a mistking and abosultely love it. Mist is a very fine mist and the pump is very quite. Only had it for about 3-4 months now but it seems very reliable.
For a veiled a mister would be better. But, depending on the normal humidity range in your region you may not need it to mist too often every day. Veileds don't need the higher humidity some other species do. There is a great caresheet for veileds under the Resources tab.
Foggers work better for maintaining a higher air humidity level in between the normal hand spraying or misting you would do anyway. Montane cham species often need this depending on how dry your area is.
I got my mistking almost a year ago and I love it. Can honestly say that it was well worth every penny. Before getting it I had 2 reptile foggers, each for just a couple months before they got loud & stopped working. Also, the fogger does not allow them to drink like they are able to with the mister. I have one of the nozzles positioned so that the mist hits the top of his enclosure just enough for there to be some water to drip down for a couple minutes after shutting off. And the extra money it cost to get the timer they have to go with it-also...well worth the money.