I would like to run electricity from my shop, which has 200 amp service, to my barn, where I would like a 50 amp box. The distance is about 250 feet. I would like to have lights, a couple of outlets, a night light and be able to run the occasional power tool in the barn.

My question is what are the pros and cons of direct burial versus conduit and what gauge wire should I use?

With out knowing the size of the barn, it's a difficult guess.

As to the advantages of using conduit vs. direct bury, I'd use conduit.

For couple of reasons, 1) depth of trench is much less. In direct bury, you would need to trench to a depth of 24" from the top of the cable to grade level.

2) Most important, if you use conduit and there is a failure of the cable, it is much easier to remove cable from a conduit then it is to re-dig the trench.

This would also apply if you need to increase the feed to the barn.

You did not indicate whether you would use 240 V at the barn but I'm suggesting you do.

Using a voltage drop calculator, you would need a 1 AWG Copper 3 wire cable with ground. Or a 2/0 AWG Aluminium cable.

Please note, that if you bring power to a remote building, you are required to provide an outside light at the entrance to the building.