Sheep are quite versatile and highly profitable if managed correctly. We run a a flock of commercial Dorper and White Dorper cross hair sheep, along with a handful of crossbred meat goats, and that's what we do for a living.
There are instances where a sheep or goat would have definite advantages over one or the other, but that is largely dependent upon what your plan is and what kind of land and grazing you will be using. A range goat's diet will consist of about 50% browse (brush), 25% grass, and 25% weeds if it is all available, where a sheep's diet on the same pasture would consist of about 50% weeds and forbs, 25% grass, and 25% browse. If you had a really brushy pasture, or woodlands with a lot of undergrowth, then goats would probably be a better fit as far as utilizing the available forage. If you had a weedy meadow or field, then sheep are probably a better fit.
Good fencing is required for either animal. Sheep are easier to contain, but need a good fence to help keep predators out. Healthy, full-sized adult goats (with horns) generally need less predator protection for themselves from coyotes and the like, but a good fence is imperative if you want them to stay on your property where they belong. If you have predators around though, both animals need good protection during lambing or kidding season since the babies are most vulnerable. Goats tend to stash their kids somewhere and go off to graze. If a coyote happens upon a hiding kid goat, he's a handy little sack lunch. Ewes stay with their babies until weaning time, but a ewe can't always effectively defend her lambs from sharp, hungry teeth and claws.
Temperament wise - they are two very different animals. Goats are more personable and love to be petted and loved on, but they are not in the least bit friendly towards other small livestock, or even other goats for that matter. Our sheep and goats are in the same pasture, and we can't pour out sack feed for the sheep if the goats are around. The goats will hook the ewes with their horns and won't allow them to eat. The goats will hook each other too, and it seems like someone is always fighting amongst our herd of goats. Woe be unto any kid goat who runs up under the wrong nanny goat - she will hook him too and dump him on his poor little head. The sheep are more reserved and standoffish, which a lot of newbies to the sheep business find frustrating. Sheep are content to stand near you and let you feed them, but they really would rather not be touched. The ewes are far more forgiving of errant youngsters as well, and a ewe will just walk away from a lamb that isn't hers rather than knocking him in the dirt like a goat would. The standoffishness is what makes a lot of people think that sheep are harder to handle. Neither is more difficult than the other, but generally some kind of facilities are required to effectively handle sheep when it is time for routine procedures like vaccinations or deworming. With a handful of pet goats one can rattle a feed bucket, and then grab whoever they need out of the mob of goats to do whatever needs done.
There are breeds of sheep intended exclusively for dairy production, like the Lacaune and the East Friesian. Currently the U.S. imports several kinds of sheep's milk cheeses, and the American Sheep Industry Association is trying to raise awareness of sheep dairying to help boost interest and perhaps create more domestic production. The most popular sheep's milk cheeses in the U.S. are Manchego from Spain, Pecarino-Romano from Italy, and France's Roquefort cheese. ASI and the Let's Grow Program actually have a webinar coming up in March about sheep dairying: https://attendee.gotowebinar.com/register/2962937926909717505
One place where I feel like our sheep really outshine the goats is in overall productivity. Our ewes consistently produce a 145% to 152% lamb crop on range pasture with minimal inputs as far as feed goes. We don't have to worry about mammying them up because the sheep are better mothers. The ewes can also grow a lamb to weigh 60 pounds at 60 to 90 days old, which can be shipped at that time right off the ewe. The average kid goat on range conditions could take 4 or 5 months to reach 50 pounds. The kid goat's overall rate of gain is quite slow, and even on feed or high quality forage crops isn't superb. We raise hair sheep, so an accelerated lambing option is there if we choose. In our accelerated lambing program our bucks are picked up and turned out so that the ewes are lambing every 8 months. They breed - gestation is 5 months - the lambs are weaned at 2 to 3 months old - and the ewes breed back to do it all again. Accelerated kidding is not an option in many parts of the country because goats in general are seasonal breeders. From March 20 to June 21 is the anestrous period for most goats in North America. I know that statement will hurt a bunch of feelings amongst hobby farm goat owners, but it's the truth. The bucks don't rut and the nannies don't breed during the anestrous without a whole bunch of jumping through hoops - artificial lighting, hormone treatments, and rain dances and sacrifices to the gods. There are exceptions to the rule, but they are few and far between.
You can learn more about the various breeds of sheep here: http://www.ansi.okstate.edu/breeds/sheep Though not all the breeds listed are available in the U.S. at this time.
General information about sheep health, management, etc. here: www.sheep101.info
And about commercial sheep production here: www.sheepusa.org This is ASI's website, and will be focused mainly on woollies running on western rangeland.
Wow thanks so much for all the info!! It was definitely useful!

Do you think some of the difference and slower growth is because meat goats in general just take longer to fill out than say dairy goats or do you think all goats in general take longer than sheep?
I'm not sure I'll get either any time soon but I hope to eventually. When I eventually move and have an actual farm if I do then it might be more for profit but for now it'd be mostly pets. Is one superior in that area?
And can they be housed together or not?
Because we have almost 3 acres but about half is the yard/grass/lots of weeds in it, and the rest is woods so there's a lot of mixed terrain of grass and scrub and I thought maybe it might be better to get some of each for the different terrains? Or no? And I'm assuming we shouldn't mow it? But would only a few sheep and/or goats be able to keep the yard down or not really?