You can reduce it to a few simple differences, because all of them will likely out shoot you and 99.5% of anyone that might ever shoot them.
Green Mountain barrels are made out of 1137 steel (this might be important to you - if you don't know what I'm talking about then it absolutely isn't important).
Green Mountain barrels DO NOT come with a breech plug installed - so order and pay for install by the vendor or buy the plug and time it in yourself.
Secondly, they have "square rifling". The arguments go on as whether square is more accurate but round is easier to clean etc etc.
Colerain barrels are made out of 12L14 steel (as note above) and they have "round bottomed" rifling (same argument).
Colerain barrels DO INCLUDE a breech plug BUT there has been enough instances where the plug was not properly timed that I would, at minimum, check or have it checked to ensure there is no gap between the plug face and the bottom of the barrel tap.
Rice barrels are made with 12L14 steel. They are available in either square (builders) or round bottomed rifling.
They are the best "finished" of the three brands (least amount of file/sanding work required - may or may not be important) - this is part of why they go at a slight price premium.
They DO INCLUDE a breech plug which I have never heard has been anything but "perfectly timed".
IF (IF) at some later date you decide to sell the rifle and IF it has a Rice barrel it will command a premium over the exact same rifle with either a Colerain or Green Mountain barrel.
Rice is probably seen as the "top shelf" barrel from any of the (mass) barrel producers currently on the market (barrels that are "in stock" at various suppliers).
(I do not include Rayle or Getz et al in that list since they produce very few barrels with sometimes multi-year wait times)
I currently shoot, in my personal rifles, Rice, Oregon, FCI, Green Mountain and Colerain barrels. From a functional, accuracy, ease of cleaning and any other number of variables I "personally" can't see a single difference between one and the other.
For me it always comes down to "who has what I want (caliber and profile), when I want it 1) is stock or 2) available in the shortest amount of time if I order.
When I wanted a tapered 38 caliber barrel, Charlie Burton/FCI barrels was the "only one" that could provide it to me in less than 2 years (took 14 months), so he got the job.
**If you are looking for a Rice barrel, call Rice. Jason carries some stock - he will ship direct to you (hey, he has shipped direct to me in Canada no problem at all on more than one occasion)