Is there something in the insulation/jacket of type UF cable that makes it unpalatable to rodents or resistant to rodent attack? Or does it need to be protected from rodent damage when run outdoors, esp. aboveground? (Say, by pulling it through IMC or RMC, just like you'd do if it could be hit by an errant weedwhacker or car bumper.)
You may be able to find a UF cable that has a rodent repellent in it, but it's certainly not standard. I have never seen it advertised on UF product packaging. I have heard that some datacom / telecom cables that claim to have a rodent repellent jacket, and I have seen those same cables chewed to bits by some varmint that didn't mind the flavor.
If you are going to run power in conduit for rodent protection, you don't want to run UF, run single conductor wires rated for wet locations, such as THWN. The only thing I can think of more troublesome than running NM in conduit would be UF. Seal the conduit well at the ends to deter the little buggers from creeping down the pipe, they can infiltrate smaller conduit than you'd think.
I'd usually rather run conduit anyway with a buried cable. If a rodent does eat your wire and it's in conduit, it's not too bad to pull a new wire. If it eats direct buried UF, get your shovel.
Rodents need to continuely gnaw to keep their front and bottom incisors sharp. Also, if they didn't chew, their teeth would grow in length to the point of interfering and preventing them from eating. It is an instinctive trait with all rodents. One way to prevent them damaging your wires is as you noted; run them through a metal conduit or plastic if they are buried. Another preventive measure is to make the item unsavory by appliying a spray made from capsium, the oil that make chilie peppers hot. I'd also set traps in the spots where the damage is noticed. It would be wise to eliminate the rodents causing the problem after the cables have been protected.