This has become an interesting thread on STOBAR/STOVL vs CATOBAR, but as far as the comparison of the ship characteristics we need to step back a second. There is a lot of focus on technology, and it does matter, but I would argue the wrong technologies are being attributed to superiority.
Russian Naval doctrine is heavily influenced by the lessons learned near the end of WWII, and is very different than western naval doctrine, particularly for carriers.
For those who never studied the differences between 1939-1943 WWII aircraft carrier doctrine and 1944-> naval doctrine, lets review a few things.
Towards the end of WWII, as fleet defense systems improved, air strikes on fleets became extremely difficult, and costly. Attacker losses mounted heavily compared to defender, and ship based defenses could cripple the attacker creating vulnerability to counter-attack. The 3rd Fleet under Adm Spruance carried almost exclusively fighters on all 15 big deck carriers, with very few bombers at all on the big deck carriers, so the combination of improved AAW defenses throughout the fleet and massive numbers of fighters for defense led to outstanding statistics of destroying attacking Japanese aircraft.
At the same time, Halsey, whose 5th fleet ran with more bombers than Spruance did, had less success towards the end of the war than towards the early period of the war, precisely because the Japanese air defenses were so much better. Even the engagement at Leyte Gulf bears this out, while the Taffy force had enough aircraft to deliver severe punishment, they simply couldn't because the air defenses were so capable. It was in fact the combination of the suicidal tendencies of those airmen and equal madness of the US destroyers that made the difference. In the end, air attacks over several days were largely irrelevant to that battle, with most of the Japanese ships sunk in that battle by torpedoes and guns, from both submarines and surface ships.
Russian Naval doctrine was influenced by this. Throughout the cold war, including through the construction of Admiral Kuznetsov, the Russian Navy was built to provide massive defense at the fleet level. The constitution of the Russian Fleet bore this out, they build an aircraft carrier to provide AAW defense, several Kiev class ships to provide ASW defense, and almost all of their cruisers were designed for AAW defense. They had limited strike power on cruisers and destroyers, but for the most part strike power was intended to come from long range bombers and massive numbers of submarines. Compared to NATO, one can see the massive difference in doctrine styles, defense vs offense.
Very long range, fast cruise missiles were developed for offensive strike power, but rather than launching these cruise missiles from the fighter aircraft on their carriers, they stored these strike weapons on their fleet, making ships and subs, not aircraft. primary strike weapons. That is why Russia lists the Admiral Kuznetsov as an aviation cruiser, just like they did the Kiev class.
The Su-33 is not a strike platform in the traditional sense anymore than the Admiral Kuznetsov is an aircraft carrier in the traditional sense. In wartime, if command of the sea was in dispute, you would almost certainly never see the Su-33 conduct any mission profile other than air defense and scouting.
In the cold war, the theory would be to keep NATO ASW assets at bay, NATO strike aircraft away, and ultimately pinpoint the fleet so the combination of submarines and land based strike aircraft could swarm NATO forces. Additionally, as a follow up or if necessary, the large Russian cruisers could deploy shipwrecks and other cruise missiles from very long range.
Since the end of the cold war, carrier aviation has changed in the west, moving to multi-role aircraft like the Hornet and Super Hornet. This reflects many things, but one fundamental aspect is the recognition by the US that defense is more capable than offense at sea, at least from the air. When you account for doctrine and technologies, the biggest differences between western and Russian carrier aircraft is the E-2, which provides a major scouting role advantage.
While people can debate the merits of various other technologies and tactics to determine whose methodology is superior, whether offensive or defensive etc, the most substantial difference in western and Russian aircraft carrier doctrines is the role of scouting, where nations like the US and France have huge advantages over nations like Spain, Italy, Britain, and Russia, all of whom rely on long range land based assets. Of the last 4, Russia has the advantage IMO only because they have superior offensive and defensive capabilities throughout the rest of their aviation fleet and surface forces, but if you start comparing Russia to the French or US, the E-2 is the game changer, and with the US the EA-6B and future EA-18G put the US in a different league, ahead of most of the worlds air forces.