http://www.naval-technology.com/projects/kuznetsov/
http://en.wikipedia.org/wiki/Soviet_aircraft_carrier_Kuznetsov
Link to some info on the Kusnetsov. It is Russia's premier aircraft carrier.
The 2nd bit, the Wikipedia site is pretty good.
That ski jump is the main problem. It drastically reduces the payload of the aircraft that takes off with it. On top of that, Russian fighter/strike class aircraft in general have always had problems with hauling ordinance in good quantity.
"The ship has the capacity to support 16 Yakovlev Yak-41M (NATO code name Freestyle), twelve Sukhoi Su-27K (NATO codename Flanker) fixed-wing aircraft and a range of helicopters including four Kamov Ka-27-LD (NATO codename Helix), 18 Kamov Ka-27 PLO, and two Ka-27-S."
As you can see the aircraft carrying capacity of this carrier is puny compared to the American counterpart. According to this, it will be carrying about ... lets say 30 combat aircraft at most. The American one can carry more than 3 times that amount.
Kusnetsov can go 29 knots. Nimitz class can surpass 30 knots. Close, but it shows you that the Kusnetsov doesn't even have a speed advantage over the US carriers and in fact, is marginally slower.
By the way, the YAK-41 was abandoned and isn't going to be in production.
As with almost everything Russian nowadays concerning the military, it looks far better on paper where you don't see the rust and the broken parts that need to be replaced... that haven't been done so in 2 years.