I doubt the Liaoning can carry 27 Flankers. China operates a carrier with one of the smallest hangar decks in the World even smaller then the one on the 42000 ton Charles De Gaulle. And at the same time China operates the world's biggest deck based fighter the J-15 a Flanker. The Russian Kuznetsov has 14 SU-33's and 4 SU-25's and another 17 helicopters. China maybe able to fit 20 to 24 J-15's and another 12 to 16 helicopters on board.
The only place I've read the Russian Kuznetsov's "14 Su-33" count is from wikipedia. I think that is an indication of the total number of operational Su-33s the Russians have, not its capacity. Most of the places I've read say the Kuznetsov class was supposed to top out max at about 50 planes, 24 fixed wing, 26 rotary.
As for the CdG vs Liaoning hangar size, Jeff did a good collection a while ago
So CdG is slightly wider but Liaoning is slightly longer. However from the videos we've seen I think the Liaoning's hangar has been slightly extended (compared to Varyag/Kuznetsov). I'm not sure if that would allow an extra couple of planes to squeeze in, who knows.
Also, plane capacity isn't only dependent on the planes you can squeeze in the hangar, but also the size of your flight deck. Not every plane will be tucked inside. I expect a good portion would be left on the flight deck and rotated in and out of the hangar for maintenance, etc.