Rotational Weight is felt more than any other weight, except maybe that around our waist imho. Having said that, I wouldn't be worried about switching bikes unless you are just looking for a reason to justify n+1. However, you could save a lot of rotational weight by switching to a lighter tire and tube combo.
When the Vittoria Randonneur Cross tires wear out on my touring bike I'll be switching to the Vittoria Randonneur Hyper. There should be a decent weight savings of ~250g and the smoother tread on the hyper will be nice. A fellow commuter at work reliably claims to have ridden his Hypers for 4,300 miles (6935km) before have to change out the tire.
Therefore, agreeing with Commodus, if you aren't trying to push the pace and want to enjoy the ride then stay with your current bike and I'd add reduce the weight of your tires without reducing the width or size of your tires by much.