Hardware cloth is easier in that it won't wooble all over the place the way chicken wire does. It's quite rigid, so it won't take as much effort as chicken wire to stretch it smooth. Also, if you could add additional pieces of wood to the sides of the run (vertical and/or horizontal) to give less space between supports it will make it easier to stretch any kind of fencing. Hardware cloth however does have sharp edges at the ends of the roll and anywhere that you have to cut it, and these edges can leave a nasty scrape if you aren't wearing protective clothing.
Hardware cloth is the gold standard for runs. Properly installed, it will keep out pretty much anything but bears. But it is expensive to cover a large run. A lot of people (myself included) will cut costs by using a larger welded wire (such as 1x2" welded wire fencing) to fence the run and put chicken wire or hardware cloth along the bottom few feet to keep chicken heads in and prevent predators from reaching through (they could still destroy the chicken wire and reach through, but in the time it takes them to destroy the wire hopefully the chickens will be smart enough to move away from the fence so that the preds can't reach them). If your chickens will be locked in the coop at night and the coop is secure, you could get away with deer netting or chicken wire for the top of the run as the main purpose for covering a run is to prevent predation from hawks and other areal predators. If the chickens are locked up at night, a raccoon and other predators can easily climb into a run but won't stay long when they don't find a meal.
