In my experience, while both finishes have some odor, standard (which was used on the decks you mentioned) is relatively mild when compared to the sharper, chemical smell that comes from a Magic Finish/Performance Coating deck. My wife actually LIKES the smell of Magic Finish. To me, it's just that "new card smell" but a touch stronger and longer-lasting. Cambric, Linen, Air Cushion, Linoid, etc. - same finish. Mostly just marketing names, though at one time they were distinctly different chemicals. (Though I will say there are a few decks out there with Magic Finish that are not labeled as such, instead using one of the more traditional names.)
If you really thought you were having a reaction of some kind, try getting another deck of the same type you're reacting to and see if the reaction is the same.
If you do discover there are some cards you're reacting to allergically, USPC does have a third finish, much less common, made of organic, recyclable materials, mostly starch. The decks using it also have vegetable-based inks and 100% recycled paper (post-consumer, I believe.) Two examples off the top of my head would be Bicycle Eco Edition and Bicycle Archangels - I'm sure there's a few more. The starch is probably corn-based (it's cheaper than most others) so even a gluten allergy shouldn't be affected by them.
Xntrix - one of these days you should write up a post or two about your card knowledge in the "Fact or Fiction" post at the top of the Plethora! It would be good to hear about the processes in making cards from someone on the inside.