Whats the advantages/disadvantages to each. Never understood why you would want 1 or the other but its time to buy new ones and figured i would ask? (for mini sprint)

The main difference is in ease of changing. To get a solid gear off you have to unbolt half your axle, remove the birdcage, wheel, etc. to slide it off the end. With a split gear you just unbolt it, take each half off and then bolt the new one on. If you rarely or never change gears it is no big deal, but if you change frequently it can be a hassle to deal with a solid gear. If you have a quick change sprocket carrier and split gears you can make the change even faster.