The Oasis lacks a daggerboard and the fins provide some additional lateral resistance when sailing across and up wind. Clearly bigger fins are going to prove more resistance than smaller ones but even with the larger fins you should not expect your Oasis to perform like a "proper" dinghy or yacht ( i.e. one equipped with a daggerboard or keel) when sailing upwind - for example the Adventure with its daggerboard performs much better on this point of sail and better overall as a sailing boat due to its lighter weight and sleeker hull.
The previous poster is correct in that you should also not expect racing yacht performance from even a lightly loaded Oasis let alone one with 2 adults on board - the sails are only really usable in pretty light winds and the sails are small and set on bendy masts so the performance you can expect is slower than you would expect from pedalling.
I recommend that you don't let these facts put you off: sailing these wee boats is very engaging and there is nothing quite like being propelled along, however slowly, both silently and without effort. If you find yourself bitten by the kayak sailing bug then the Oasis is a very good craft to start tweaking on e.g. By adding stays to the rig and/or more sail - it has enough ballast, beam and waterline length to cope with additional canvas (another mainsail making it into a schooner or a jib giving it a "normal" yacht sailplan and a real challenge to manage especially singlehanded) and extra rigging. If you find the sailing experience underwhelming then you could sell your sail or keep it and get yourself an Adventure for its better sailing performance.
If truth be told I guess that many if not most people would probably look to upgrading to Turbo fins as their first upgrade, though. But if you are already intrigued by the sailing potential then you may not want to take this route. Consider how often you get reasonably light winds in your playground - you need enough days of lightish winds to get the most out of your sail (N.B. flat calm is no good: you need a definitive breeze but just not too much of it!) otherwise the turbos may be a better bet. Also consider your crew (or is it your Captain?!)... If they are not into the pedalling thing then they may not be particularly impressed with bigger fins (faster yes, but also more effort)... If the crew likes taking it easy then they might really enjoy the sailing. But if you singlehand your Oasis a lot then you don't really have to consider a crew do you?!
Either way both are excellent upgrades... There, i said it.... "Both".