I've not ridden any of the new ones, but have been on plenty of older 250's and 300's.
IMO, the main difference is the 300 has much more low end power, some more mid range and also a bit more top. When traction is perfect, it will pull a couple of lengths on the 250 in a drag race through the gears. In the tight stuff, you can ride it a gear high and really chug it like a big 4 stroke. If you are riding super technical trails (the kind no organization besides Last Man Standing would hold a race on), there is a lot to be said for being able to climb anything at low rpm in 2nd or even 3rd gear. In the open stuff like fire roads and desert, the 300 will run head's up with the modern 450 4 strokes, while you will have to flog the 250 much harder to keep the pace.
All that being said, I personally prefer the 250, because it has enough power to do anything I want, and it does not tire me out as much when riding a long day of single track.