I go from a heavily leaden ( with emphasis on the lead- 35lbs) commuter, which I ride daily a minimum of 22 miles and usually add on more with grocery shopping and other errands, to a relatively light old custom steel framed road bike (21 lbs).

I've often given thought to the same question you asked and here's what I've observed:

Commuting every day on a heavy bike loaded down with the stuff I have to carry definitely keeps me in pretty good cardiovascular shape and the legs stay pretty strong. But I am usually travelling at a slower, more moderate speed and am pretty consistent in how hard I am working. Unless I'm late or inspired I don't even approach my max aerobic threshold since in the morning I'm just waking up and on the way home I just want to unwind from my day. I do keep a pretty fast (80-90rpm) cadence on the bike, however, and I think that has some payoffs on the road bike.

When I get on my road bike in the winter, like today, and I haven't been putting that many road miles in I feel slower, more lumbering and the bike feels jumpy and almost too light. After a few miles I start to get my form and the feel for it and I can feel that I haven't lost my general fitness but really I'm lacking what I call "snap". I just feel like riding the way my body is used to- just plodding along- with not much speed. Hey, it's winter, I'm in hibernation mode.

When I'm riding more on the road bike in the spring, summer and early fall and I'm getting faster that's when I notice that my stamina has improved from doing the commuter every day. I can use the commutes as training miles either as a base or just "time on the bike" and make my road rides more specific for training- like intervals or hill work etc. Then I'll start mixing it up a bit even on the commuter and will find myself flying along in jeans and a t-shirt carrying 25 lbs of crap in my milk crate pounding along with the traffic at 25 mph every once in a while and that's really when it gets fun.