Why is it that the jacket would fill up but not a dry top?
Does the jacket have latex gaskets?
If not, it will let water in. A dry top or even a semi dry top will have gaskets or tight fitting neck/wrist seals.
If you plan on being in the water (ie swimming) a lot I would not even recommend a semi dry top, but a full dry top.
I think I modified my post as you were posting your reply. Is the difference between a semi dry and a full dry simply that the full dry has the gaskets while the semi only has tight cuffs?
Yes, semi dry sometimes has a tight neoprene, sometimes just a fold with some velcro, whereas a full dry has latex gaskets at the neck and wrists.
In any case, either a full dry-top or semi-dry top, if you swim, they will get wet from the water getting in through the waist. They are designed to keep you "dry" if you stay in your boat with your skirt tight to your cockpit, and body.
Once you leave your boat, it won't prevent water from wicking up your shirt from the waist past your skirt, and getting you wet. Since your in a kayak, and wearing a skirt, the neck and sleeve seals/gaskets will prevent the sleeves and chest from flooding and making swimming difficult.
If you plan on swimming a lot, either briefly or for extended swims, seriously consider a farmer john with a paddle jacket top if it is a cold day, or perhaps just a neoprene vest and shorts.
If you are in an open boat (tandem or otherwise) then the lack of a skirt makes any paddle jacket somewhat more likely to fill with water, unless the jacket has a double tunnel you can cinch down to keep the water from flooding in at your waist.