Of course the main big thing is, how good a job has been done on either
If you want a really digproof
buried fence, it needs to go down 18" (possibly deeper if you've already had significant problems with dogs/foxes digging under), be made of as heavy-gauge a material as you can get (for which reason, chickenwire=bad, hardwarecloth=enh; you want something thicker, really) and galvanized.
Pros of burial: Works ok if deep/strong enough. And leaves nothing interfering with your use of soil surface along run, if you wanted to garden there.
Cons of burial: Huge amount of labor involved. Not practical in all soils/sites. Buried mesh will disintegrate (you can pour concrete instead of burying wire... but that is very expensive and laborious if you're doing a proper depth, and will frostheave and break up in northern climates). Yes, galvanized wire rusts. The heavier the gauge, the longer it takes til it's weak enough for something to break through, which is why I strongly advocate a heavy gauge wire mesh for this purpose. But it'll ALL rust eventually. Which leads to the final con, you will have no idea what kind of shape the stuff is in as time goes by, inspecting it requires digging, and replacing /repairing/bolstering it will require the same big excavation that you had to do in the first place.
If you're going to put in an
apron, it should be heavy gauge galvanized mesh (just like a buried fence) (although, light gauge mesh can be easily inspected/replaced if necessary) and should extend ideally 2-4' out from the base of the fence, depending how many of what sort of digging critters you're concerned about. And it needs to be well fastened into the ground, by thoroughly pinning it down and letting the turf grow up through it, or by covering it with big pavers or large rocks or concrete rubble, or by peeling back the turf and laying it underneath. In particular the *edge* should be concealed, both to keep you from hurting yourself and to keep that one in a thousand predator from having A Thought.
Pros of an apron: Not much work, compared to burying the bottom of the fence. Easy to inspect/repair/replace as desired/necessary. Suitable for virtually all situation, even if you are on bedrock or tree root filled earth.
Cons of an apron: prevents gardening along run. May be some work to fit if there are lots of tree trunks or fenceposts or whatever where the apron would have to lie. [Also, not a concern for hardly anyone, there are one or two extremely experienced, 'professional' red foxes in the world that have learned to back up and tunnel under. You probably don't have one of these, but if you do, you want either a WIIIDE apron or a DEEEEEPLY buried fence (because foxes can also dig *down* several feet with ease...)]
As long as the apron is really tied to the ground well, not just lying there loose, and the edge is concealed/fastened well, it is as safe as a buried fence.
So it mostly comes down to, which do you want to install and live with.
To me, and I *like* digging holes/ditches, it is a no-brainer, the apron is a lot better bang for your 'buck', for most situations. But, personal choice.
HTH,
Pat