(Grabbed from Jenvey without permission LoL)
In the beginning, at the start of time, when the universe was young, carburettors and mechanical fuel injection were the only available choice to fuel a racing car engine. Selection of air valve type was simple and, apparently, carved in stone: carburettors used butterflies and injection used slide throttles. Bikes and their history are a special case but what follows is true for any performance 4-stroke petrol engine.
With the advent of electronic fuel injection and a more adventurous (better funded) approach from the leading engine designers, it was discovered that butterflies, whilst sometimes (but not always) giving slightly less power than slides, inevitably gave better lap times. The explanation was simple; butterflies give more progressive throttle control, improved transient conditions and aid mixture distribution.
As a result of these discoveries most (possibly all) of the leading car race engines switched to using butterflies. Lap times continued to tumble, but there was a problem brewing for the future.
As peak RPM increased year by year, the required induction system length reduced. At the same time, the ideal butterfly to valve distance increased. Over about 14 - 15,000 rpm, the butterfly needs to be outside the induction system - clearly useless. Enter the barrel.
The barrel has some, but not all of the attributes of a butterfly. Opening is reasonable progressive and, like the butterfly, it is easily packaged. The great advantage is that it can be made as a continuation of the port shape (slides would overlap) and thus be placed near or even in the cylinder head, allowing for a very short system to suit the 18,000+ RPM which is now common. Any compromises are offset by the sheer power available at these RPM. It follows that barrels on a sub 14,000 RPM engine get the compromises without the benefits.