Varian Wrynn was a card which a lot of people thought was going to be huge. It certainly has the potential for blowouts and no doubt there have been some hilarious moments with him. Unfortunately he saw virtually no competitive play because he has some serious problems.
Wrynn also doesn't gain you the battlecries of any minions he puts into play, which is sad, but even then he is still very powerful if played right on time on turn 10. However, the game of Hearthstone goes from turn 1 to turn ~25 and Varian is only playable on turns 10 through 16 or so.
All is not lost however because there is a new card that appears on the surface to be similar to Varian, but which avoids the severe problems Varian has.
It seems like faint praise to say "This card won't lose you the game when you play it", but that is actually the biggest factor here.
I also just like Y'shaarj better because you can build a deck around it. Varian is random so aside from filling your deck with minions (which isn't a deck that wants to get to turn 10 anyway) there isn't much you can do to try to maximize his power. Y'shaarj on the other hand can be put into a custom deck with a bunch of high powered minions without battlecries that will make him extremely dangerous. Imagine, for example, a control warrior that runs Sylvanas, Thaurissan, Ysera, and Ragnaros along with a huge pile of removal and weapons. Y'shaarj is *ludicrous* in that situation no matter what he pulls from your deck, and if he isn't removed on the turn he lands the game is absolutely over. I don't know for sure that such a deck is actually a good plan but I really like the way that you can use Y'shaarj to search out specific minions if you want to. That feels like it will generate some cool archetypes even if those archetypes aren't really competitive.
But it does feel to me like Y'shaarj is just a big upgrade even without that customization element factored in. Even on turn 10 he is +3/+3 bigger than Varian and he has the potential of winning more if left in play. Varian might, for example, draw 2 cards and put a minion in play, but +3/+3 is as good as drawing two cards costwise and Y'shaarj gives a minion too. Even where Varian is good Y'shaarj is just as good, and Y'shaarj avoids the times when Varian is completely dead. On turn 10 both of them are terrifying. On turn 20 Varian is worthless, and Y'shaarj is still a serious beating.
So is seems to me that the question is not if Y'shaarj is better than Varian because I think unequivocally he is. The question is whether or not that improvement is enough to make Y'shaarj a real contender. My guess is that the answer is yes. There are going to be lots of decks with old gods in them out there so I think an awful lot of games are going to turn 10, and if you are definitely going to get to play Y'shaarj then he is a real monster.
One other thing that should be kept in mind is that Y'shaarj and N'zoth (another 10 mana Old God) both work very well with similar deck types. Both of them work ideally with deathrattle minions, so a deck with 10 deathrattle minions, a bunch of spells and/or weapons, and Y'shaarj and N'zoth as finishers seems plausible. Y'shaarj might fetch N'zoth, which would suck, but you gotta take risks sometimes. (And if your disaster case is that you put 15 attack worth of minion into play in a single turn, that isn't so bad, really.)