Both are awesome cars and have great performance, with the M3P having the edge in both speed and handling compared to a 90D (though a P90D is faster). One of the major distinguishing factors between the two is size. I've found the Model S to be a little more spacious in the backseat for family daily driving than the 3. In my opinion the back seat of the 3 is ironically more suitable for adults than kids, due to the need for insanely bulky car seats for kids. The hatchback of the S makes for very convenient access and cavernous storage, so it clearly wins in cargo capacity, though the trunk of the 3 is quite spacious and perfectly adequate for most uses.
If you'll just have adults in the backseat occasionally and don't have kids, I might actually recommend the Model 3 to you (some Model 3-owning friends of mine with kids who find the backseat perfectly fine might argue this point with me). The overall technology in terms of the touchscreen computer and autopilot technology on a new M3P will be superior to a 2015-2016 Model S. The Model S is also quite a big car and the Model 3 might be easier to drive and park on urban streets. The handling is certainly a little more nimble. I just drove a M3P this past weekend and was pretty impressed with its agility compared to my Model S P85D, even though the crazy acceleration is about the same.