Straps.....gloves are for pussies. You should train your grip, and you shouldn't become dependent on straps for all of your pulling, but the point of shrugs is to overload the upper back with enormous amounts of weight. It is a short-range pull and you should shrug much more than you deadlift. All that considered, you want your upper back to be the limiting factor, so I'd suggest straps.
Also, man, don't worry about your hands taking a beating. It'll make you tougher physically and mentally. You're gonna get a lot of comments on here, but I am glad I got here first.....gloves are for pussies, and that is the least offensive way I can say it. The only thing gayer than gloves are those pads some people place over the bar to squat with, lol.