While I have gone camping with cloth diapers (the campground had a little laundry machine), it's definitely easier/less hassle to use disposables. We generally use disposables for the actual traveling (if it's more than a few hours), and then what we use at our destination depends. If I'm going to my aunt's (3 hour trip), I'll use cloth if it's a short enough trip we won't have to do laundry, but disposables if it's longer. Going to my mom's (12 hour trip), I'll use disposables for the drive but cloth at her house. I find cloth is more reliable for us though, all the sposies we have tried leak, so we err on the side of using cloth more often than not. (Though last time we tried a new natural brand that wasn't 7th Gen and they worked better.) Going by plane it would really depend on how much other luggage I had and whether I was by myself or with DH.
We're going on a 12 hour trip in a week and a half (with a full day stopover that has no laundry) and plan to do sposies for the drive/stopover, and cloth once we're there. I'm not sure what we'll do with our older daughter though. She's technically been out of diapers since 23 months, but because of allergies she still has accidents, and when they happen they happen a lot. So if we brought cloth and she had accidents we wouldn't have enough to last the 12 hours + stopover. But if we bought sposies (assuming she would even wear them), we could end up with a lot of extra diapers lol. I'm erring on the side of sposies though, because it's hard to keep her totally dairy free while traveling. (We just discovered the allergy very recently, and honestly we're not super strict about it when at other people's houses yet, because it doesn't make her sick at all and people are still getting used to it.)