Buzzard is still a card though correct? So you have to make a spot for it in you deck. The card itself gives you no advantages and is still a -1 in terms of card advantage. The card itself also rarely trades with another card and can be cleared by every aoe and several hero powers.
Buzzard plus UTH is a 2 card + 4 mana play that gets you somewhere between 1 and 6 cards back. You need at least two minions on the field for the hunter to replace the cards in hand (like novice for instance) card advantage is only gained after those 2 cards. That also assumes you can put that combo together which in many games you can't.
You are misunderstanding card advantage.
Cards in-play + cards in hand - opponent's cards in play + opponent's cards in hand = card (dis)advantage. It is (usually) a good way to measure how well or poorly you are doing in a CCG. Buzzard is a card in play, so you do not loose or gain advantage by playing it; granted your opponent may be in a position to kill it for free (ie. he has a minion on the board or is a Mage). UtH does not stay in play, but it also puts cards into play, so you only loose card advantage with it if you play it when your opponent has no minions. Also granted, those hounds may die fairly quickly because they usually only have 1 hit point.
But combine the two together - if your opponent has as few as three minions you get three hounds in play and three cards in your hand. Even if we count Buzzard against the Hunter, that's a +4.
@OwlRaider: Nice opinion. Try backing it up with actual points next time.
I understand card advantage you just don't know how to apply it. Minions on field only matter if they can trade with other cards. If they don't then they don't count for !@#$.
Lets say you are playing a druid (most common class) Neither of you play a card before turn 3 and the druid plays a Harvest Golem on turn 3.
You: 6 cards 0 minions=6;
Him 6 cards 1 minion=7
You play Buzzard + UTH
He kills your buzzard with Golem End of play
You 1 minion on the field + 6 in hand=7 (Stats on field 1/1)
Him 1 minion on the field + 7 in hand=8 (Stats on field 2/1 with 2/1 death rattle=4/2 value)
In this scenario you haven't gained a card advantage but have lost board control. Druid goes on to clear your board with hero power increasing card advantage and finishing round 4.
Turns aren't just your actions but your opponents reactions to your actions. Only then can you calculate card advantage.