Hi Mic--I'm not Cathe, but..........I actually have some pretty strong opinions on this, & as always I'm happy to share.
During the week I split up my cardio & lifting, but this is only b/c of time constraints. My preference is actually to do cardio BEFORE lifting, for a variety of reasons:
--you get your heart rate up w/the cardio, & can keep it up to some degree if you lift right after, so you can burn more fat
--your muscles get nice & warmed up if you do cardio first, thereby reducing injury risk & post-workout soreness
--cardio is more important to me than weight training (although I enjoy weight training more), so if I'm gonna expend most of my energy on half a workout it'll be the cardio. Also I'd rather finish w/what I enjoy most rather than start w/it. I just can't imagine trying to look forward to a cardio workout after lifting all those weights! I'd never make it!
Anyway, those are my reasons, but I do work out 5 days a week, & 3 of those days are either exclusively cardio or exclusively weights. I don't think there are any drawbacks to splitting the workouts either and, as you mentioned, there probably are some benefits b/c you'll feel stronger during each workout. But personally, I think doing cardio after weights is probably the least efficient way to do it.
So much of it depends on your schedule, your goals, & your genetics. My suggestion is do what works best for you!