There are pros and cons to anything. It depends first on your run size -- if you want to use chainlink (and both the things you mention *are* chainlink, of course), you can use kennel panels for small runs but if you're thinking in terms of a large area it pretty much has to be properly-installed chainlink fencing.
Personally, I like either well-installed chainlink (either fencing or panels) or heavy-gauge welded wire 1x1". Heavy gauge 2x4" welded wire's a pretty good option to consider too. On any of the above, you'd want 1/2" hardware cloth or 1/2" chickenwire (NOT the common 1" chickenwire) run along the inside from the ground up to 2-3' or so, to prevent reach-through; and either some of the fence buried 18"+ into the ground, or (my preference) a 2-4' apron of same lying on or just under the ground outside the base of the fence.
None of this will keep climbing predators or hawks out, of course. For that you would need an appropriate top to the run.
There are lots of ways to do it, though, and choice depends on personal risk-tolerance philosophy and what materials are handy.
Good luck, have fun,
Pat