What is the difference between the full zip-up and pull-over jackets? Is one heavier than the other?

Depends on which Ike you have. Some have different linings.

I rarely wear the pullover because there is no way to adjust for ventilation if you get warm.

I find them to be similar in weight and ability to keep you warm (not). In our area in Atlanta, most fastpitch umpires have gravitated toward the pullover, as most think it looks more professional and easier to deal with when wearing the chest protector. More slowpitch umpires buy the zipup, for the reason Mike mentioned, the ability to adjust the zipper for a bit of comfort adjustment.

Fortunately I have one of each. Then if weather might warm
a bit, I can switch to the zippered
one.

Pullover
 

I like the pullover myself, but...either is fine. Neither will keep you very warm in cold weather, but...

And I have used Camp-Dry on mine for waterproofing (not that we ever have issues with rain in Seattle).

I don't understand either of these opinions. I think the zippered jacket looks very professional, and it is superior (IMO) with the chest protector - easy to put on and take off, and can be adjusted for ventilation. JMO, of course.

I have no serious personal opinion about it, just commenting on it. I think the major driving force was a former UIC who was very vocal and arbitrary about his preference in fastpitch. With him being of the larger persuasion (3XL to 4XL, depending on the year), I suspect the pullover maintained coverage better, without a zipper working down or chest protector showing.

As I mentioned in another thread, I don't wear a chest protector, so the pullover has always been fairly simple for me; and if it kept that UIC (and subsequent UIC's) happy, why not?

So it seems it really is just a preference in appearance, not in warmth?