Tethering usually ends poorly. That has been my experience. Possible outcomes can include, tangled on the tiniest weed stem, wrapped around legs, broken legs, hanged animals, and predator meal on a rope. Anchoring so that it doesn't come loose or tangle up and so that they can reach water is always a challenge. Sheep and goats are both herd animals, so they like each others company, try tying two out and having one pull up his stake if you want to see a real tangle.
As far as fencing, if it has overhanging trees or brush, goats can be hard on it, they will stand up on it and eventually ride it down. Sheep aren't as bad for that, but will reach through it. They can end up pulling steeples out, and eventually breaking wire here and there and popping through it like water going through a sieve. Sheep and goats with horns, as well as wool sheep can get stuck in woven wire, possibly dying there.
Electric fence can be a good option, electro net is easily portable for unlimited grazing configurations. Electric can be less effective on sheep with heavy wool. Some goats can jump. Nigerians and any of the swiss breeds particularly. There are goats out there that can stay in three strands of electric wire.
Male sheep or goats can be aggressive. In my experience sheep a little more so. Rams generally back up and ram, bucks will rear up and hit down. They both indicate their intentions with posturing if you are cued in, but a sheep is more likely to get a cheap shot below your field of vision. Horns can be dangerous on either, but most rams curl tightly with blunt ends, goat horns can be like daggers and sweep out. With proper handling not really an issue with the aggressive males, but something to think about. Many breeds of sheep don't have horns, the majority of goats will need to be dehorned if you don't want horns. Male sheep smell a little more funky,all sheep tend to have some odor. Male goats in rut usually smell horrible, female goats tend to not smell much at all.
With grazers versus browsers, you are likely to start with good goat pasture and end up with good sheep pasture. If you ever decide to do both, remember that they can impregnate each other but these pregnancies don't advance to full term, usually not lasting anywhere near long enough to even stimulate lactation. Such pregnancies with their associated abortions can cause infection.
Goats can have a tiny bit more "personality", they tend to be a little more independent and interact a little more with humans, while sheep tend to be more herd oriented and single faceted, with less individuality. Generally. Either one can be wild and crazy or in your pocket tame depending on handling.
Neither is particularly resilient when managed improperly, some people tend to think that goats are "tougher" but that is not really the case. Sheep with wool can take cold wet weather without shelter, but would need shade and shearing in hot weather. Goats don't like rain at all and will seek and use shade in hot weather.
It is probably easier to find good goat hay in most places than good sheep hay, sheep will waste a lot of stems, but while goats love hay with some stemmy weeds, neither is particularly fond of the real strawlike grass you will find in first cutting hay. Second or third cutting is better for both, but is usually snatched up at highly inflated prices by horse owners, whose animals absolutely don't need it if they aren't being bred or worked hard.
At one time, finding a vet that knew the subtle differences between sheep and goats was hard, they had plenty of information on sheep, but little on goats. This has changed with the increased popularity of the boers in 4-h show circuits. Before that, goat owners were either very savvy dairy oriented people that did their own vetting, or they didn't view their goats as worth giving veterinary attention. If there is much commercial sheep production in your area, it might still be a tiny bit easier to find a capable vet should you need one, and there has been a ton of study done on sheep compared to goats in this country, historically, so even a vet that is not into large animals as much might be of more help if you have sheep.