There are 4 Disney Mini-golf courses on property located at two different locations. Fantasia Gardens located next to the Swan and Dolphin and the Winter Summerland course located in the Blizzard Beach parking lot. All four are fun to play and better then any mini-golf you will find off property in Orlando.
Fantasia Gardens "Gardens" Course is the best mini-golf on the property. As expected it is themed after the movie Fantasia. It's very interactive and kid friendly. It is the perfect mix of challenge and disney theming. The holes have multiple levels in the sense that often you are putting up a large slope hoping it comes down in the right place on the other side. You also put downhill often and have to make sure you have your speed correct. There are also special effects on almost every hole. Some holes it really jumps out at you and some holes it is more subtle. Regardless, it is really well done. It really is a great experience that both young and old can enjoy. However, because of this, the waits are quite long (1+ hours) to get on the course during peak times. Due to this, the rounds move very slowly. There are a lot of families with 4-6 year olds who are playing who take 10+ shots on every hole. It is quite common to have a family play so slowly that there are 3+ empty holes in front of them. If you notice a situation like this don't feel scared to skip a few holes and get past the bottleneck then go back and play the holes you missed. (Just make sure you do not play the 18th hole until the very end because that is the ball return hole). As someone else mentioned there is not much shade and the astro turf acts like a hot plate making it a very hot experience on sunny days. I highly recommend bringing drinks with you (you can bring your own soda or beer on the course). I say this politely, if you are a family that has one of these younger kids that aren't quite ready to play at a normal pace, give your child a head start on the holes that allow it. Let them tee off from halfway down the hole and turn the 10+ putts into 5ish. Everyone behind you will be very grateful and your little one will still have a great time.
Fantasia Gardens "Fairways" course is not your typical mini-golf course. It is designed like an actual miniature version of a real golf course. The holes are 30-75 yards long and have "sand traps" and water in the way. 10+ years ago the fairways course had actual sand that made the course a real challenge but people were trying to hit out of it and spraying sand everywhere, so it was removed. Now the sand traps are sloping holes that can mess up your score. The employees at the course will say this, but I'm going to stress this here. This course is NOT for young children. I would easily say that you should not play this course if your kids are under 10 and kids in that 10-11 range should want a challenging experience to have any chance at enjoying this course. "Par" on this course is 72. While experienced golfers will have no problem shooting under this number, inexperienced golfers could easily find themselves frustrated and taking 10+ shots on most holes.
Winter Summerland I am going to discuss at the same time because the courses are very similar. One is winter christmas themed and the other is themed like Christmas in July. Both are much easier then either of the Fantasia Gardens courses with mostly flat holes that have obstacles in the way like a traditional mini-golf course. IMO both of these courses are the most friendly to young children. Like I said, the holes are flat and the obstacles aren't very complicated. Also, who doesn't love feeling like Christmas while playing golf. These courses have much more shade so it is a better option on a hot day. The courses are fun and have the expected level of Disney themeing.
In my opinion, there is no contest on which location is "better". Fantasia>>>Winter Summerland. However, if you are looking to play mini-golf at WDW, you are going to have a good time at either location.