A lighter/sportier bike will FEEL faster, even if ridden at the same speed as the cruiser, and will be easier to get up to speed. Such a bike would probably be a bit easier to ride at a faster speed on clean pavement, but the nature of your commute probably kills any advantage that would bring. I'd say a sporty hybrid or cyclocross with 32c tires would be the best mix of speed and versatility for your commute.

All of that said, I doubt you'd see any significant time savings (unless the slight increase in speed alows you to "make" timed lights that would otherwise stop you). Stoplights are the pace equalizers.

Just this morning, while in my normal commute groove, I blasted past a guy on an old schwinn while riding along a lengthy east-west road near downtown (i.e. lights every 1-2 blocks). He rolled up while I was waiting at one of the (notoriously) longer lights 10 blocks later.
It is the nature of urban riding.