I'm in SE Texas. I have cattle and have 2 neighbors have cattle. In 25 years, this is what I have experienced and learned:
If the fence is within property lines, the owner has the right to do anything he wants, and has no right to ask for cost sharing. If it is on the line, check your laws. Where the benefit is one sided, it would be unreasonable to split the cost, unless law says otherwise. Instead, if you want to be a good neighbor, a limited amount can be offered, but I suggest giving input of what you want or do not want. Put that as well as maintenance in writing for the memory and good of all.
I have tried electric wire thinking it would save me time. Over and over (and over), the fence was disabled - by weeds, falling tree pieces, deer, cattle pushing each other. Never again - PITA.
I have tried to maintain barbed wire, sometimes to the point of adding extra wires to keep heads from poking through - as in 9 wires in some areas. I dislike barbed because of the heads-sticking-through problem, which puts pressure on the fenceline when the neighbor's cow eats my grass. Makes me stop killing weeds on my side. Solution is field/hog type fencing, which also permits posts to be up to 20 feet apart. I like 15 feet. Never leaning because never pushed. But it needs a 4 point barb wire on the bottom and top to keep heads and necks from tunneling or pressing down.
Neighbor #1, the largest, has cattle that keep getting into my pasture, especially if their grass situation is poor. Todate, I have returned well over 30 animals - I trap them then call him to come get them, but have been known to take them to his place just to get them out of here. Problem is old barbed wire fencing that is always in need of maintenance. A down tree or situation where they can (and will) jump over are most common. Legally I can charge him a trapping fee, say $100/head. I should do this, for this guy will never do anything if I complain that his cows are in my pasture. He seems to depend on me to help him out, and never does anything with the fences we share.
Neighbor #2, has a grazing lease and his motto is never do anything unless forced to. All of our common fence was brand new 5 wire 4 years ago, paid by the landowner, and is in sorry shape with lots of sloppy unprofessional fixes. When the fence was replaced, the landowner wanted things done his way, so he paid it all; didn't even tell me beforehand. Hired a dozer which took out all of the fencing and associated trees plus 30 feet of thicket on his side. My side was clean. I asked him to leave a tree here and there, but ignored me. I have learned that if you don't want trees to take down fences, make sure nothing is close by, so I ended up liking the clean fenceline. The barbed wire is a problem. 6 wire would be better, but the best is field/hog wire. The fence is now leaning my way because I have no cattle in my side along that fence. His bull came through once to smell my passing cows by stepping through that fence. He made the wires look like rubber bands.