Well one difference that is obvious is that the Contemporary is the closest resort to the Magic Kingdom and the only one with a walkway that goes there.
Now if your also wondering about their Club Level service I have stayed Club Level there on the Atrium Club 12th floor multiple times and each time it was a positive stay. However and this is true of any WDW Resort or Club Level stay, just because at the Grand Floridian gave you all those things does not mean it will happen somewhere else. Yes you can put it on your reservation that your celebrating a birthdays and an anniversary, however I am sure a lot of other guests are doing the same and WDW can't do something for everyone.
When it comes to other differences if you happen to have a car the Contemporary self parking lot is a lot better because it's a short walk to their lobby, where as the self parking lot at the Grand Floridian is across the street.
Finally when going to Epcot from the Contemporay you take the Resort Monorail one stop to the TTC, then switch to the Epcot Monorail. From the Grand Floridian when you take the Resort Monorail it stops at the Magic Kingdom and Contemporary before arriving at the TTC.
Also when the Contemporary and Grand Floridian share Bus service, the Contemporary is always the 1st stop and Grand Floridian is the 3rd stop after the Polynesian.