It should feel different and you should be faster on a lighter bike - its all about power to weight. If you are lugging around a heavier bike, your power to weight ratio will be down. When you switch to that lighter bike you haven't changed the amount of power you are putting out, but because you weigh less you will go faster. It is a great psychological lift even if it doesn't have other benefits (I don't claim to know for sure that it doesn't, but I suspect it probably does not have a functional advantage)

So I can do the same workout on my rain/commuter bike, with a full messenger bag and I will be moving slower for the same power output/hr than would happen with my race bike. It doesn't mean the workout is any different, just the speed. Now if I need to say do slow cadence work (sort of a bike variation of weight training) that may be easier to do on my heavier bike because I wouldn't need to gear up as much to maintain a low cadence, but as far as I can figure there isn't any other advantage.