As straight kayaks, there is not much difference in draft. Typically loaded both probably draw about 4". Freeboard varies by boat and location (see pics below). Both have similarly shaped tri-lobed hulls with with very moderate rocker.
Being 4' longer and 2" narrower, the Tandem "Adventure" is about about 36 lb. heavier (according to my scale) and somewhat faster (with 2 pedalers). I agree with fusioneng that it is potentially the fastest Hobie, with the Adventure a close second, Oasis (with 2) third and Revolution 13 fourth. The TA has more deck space and 50# greater capacity, so is relatively spacious.
Both boats are very stable (TA more so); the Oasis has an edge on turning and would probably be better in restricted areas where tight maneuvering is required. With more deck space, the TA has more load options. Significantly shorter and lighter, the Oasis offers more loading and transport options for most people.
Sailing, there really is no comparison. The Tandem Island is an exciting and versatile sailer whereas sailing is an afterthought with the Oasis.
The current Oasis bears little resemblance to any of the three older Oasis models, so one must be careful in characterizing the new Oasis based on any of the older models. Tandem Adventure at slow cruiseOasis sprinting