From my own relatively unscientific point of view, I'd say it depends a bit on what lenses you already have, and what you find most important, where you're goinge, and a bit on budget. I like the idea of easier cheaper access to wide angles on FX, but DX is cheaper to start with, and I like the size of DX cameras better. My first digital SLR, a D3200, is very nice for traveling, compact and capable, and its cheap lenses perform decently. My current one, a D7100, is still fairly compact and provides fine images for my taste.
In theory, at least, FX will give you better low light performance, but newer DX cameras have become so good that this may not be a factor in ordinary use, even though the relative advantage will always be there.
Since one of my favorite photo occupations is chasing bugs, I find the DX format nice, allowing pseudo-macro shots with relatively longer lenses (and yes, I know it's just cropping, not really "reach," but on a high-pixel DX sensor it stands in for reach rather nicely). A cheap D3200 with a cheap 55-300 telephoto can nearly fill the frame with a butterfly from four feet away.
One of the greatest drawbacks, I think, to the DX format is the small viewfinder image, especially in the lower end cameras. The D7100 and its ilk are pretty good, but the D3x00 and D5x00 are pretty much stinkers when it comes to manual focusing, unless you use a magnifying eyepiece, and though live view helps, it is often very inconvenient. If you do macros, or use manual focusing lenses a lot, it would be a good idea to try various models to see what viewfinders are acceptable. The cheesy viewfinder is one of the main reasons I forsook the D3200.
If you expect to travel a lot, a smaller camera is very nice to have. I've been all over the world with a D3200, and just got back from Africa with the D7100, and they're easy to pack and easy to carry. The lenses are relatively smaller and lighter too usually. Though part of me would have loved a Dx for this, the smaller DX cameras also have the advantage of being less of a disaster to lose or break. I bought the D3200 initially partly because I figured if it dropped in the ocean or got stolen or eaten by wild animals, it would not be quite the same sort of disaster.