The major differences are in the suspension and brakes. The Sport models have a firmer suspension tune, which is not necessarily a good thing if you live outside of a country like Germany with pristine roads. Sports also have spiffy-looking Akebono fixed-caliper brakes with huge (~14") rotors -- four-piston in the front, two in the rear. They grab like he-double-hockey-sticks and are quite powerful, but the standard ceramic pads they pair them with are prone to quick (and dangerous) fading under hard use. They're not for the track unless you swap in the Infiniti performance pads, available at the dealership.
Sports since 2005 also include a viscous limited-slip rear differential (VLSD), which is to me the most valuable of all the performance improvements. Infiniti has not announced whether Q50 Sports will still have a VLSD. (I have made no secret here I think they are morons if they leave this out.) You'll also get magnesium paddle shifters. A few preproduction non-Sport Qs have had them as they rotated around the display at various auto shows, but the Q50 build site indicates they're only available on the Sports, and I think that will continue.
Sports also include front seats with more aggressive bolstering and more power adjustments for the driver's seat.
One man's opinion (mine) is that the G/Q is a sport sedan, and sport sedans should be sporty. So I sport mine up to maximum factory sportiness. I do not add wings or spoilers or 22" wheels or 3" drop kits, so the factory Sport tune is as sportified as my car will ever get. YMMV.
That being said, adding the 19" Sport wheels with all-season performance rubber to a non-Sport Q is a mighty tempting option for those of us getting a little older and thin of backside. I did not do that this time around when I settled on a Q50s, but I have a feeling that day is coming sooner rather than later.