Bikes are fun period. There are advantages to both sorts of bikes too. Finally, in almost every case the rider is the limiting factor for performance.
Light bikes require a lot less work to flick over in a turn, handle rough and loose surfaces better, and are much less tiring to ride aggressively. They also get blown around by the wind and are less comfortable for extended straight line riding.
Big bikes are fun to pull out of a corner on the gas, can be ridden in a "point and shoot" style, and flat out amaze with their acceleration. However they really punish poor riding and can be incredibly tiring when ridden hard.
After taking my big bike to the track, I realized that I just wasn't going to have the same sort of fun on the street on that bike. So, I have plenty of fun on and off-road on my little bike. I can push the bike hard at legal speeds, which is what entertains me.
In short, figure out your priorities and how much you are willing to compromise them (or buy more than one bike).