The idea of a Cornucopia-esque card that rewards variety is good but I guess that this it is too strong.
Suppose that you play it with 5 cards (this is conservative, playing an action card after handsize attacks happens less frequently than playing it after you have already played other cards that increase your handsize) in your hand. It draws 4 and if you now have two copies of a good card in your hand this is akin (slightly better as the other player cannot make you discard two arbitrary cards) to a Supveradvisor (2/4 instead of 1/3) which is probably a good 4 / weak 5.
Now if you have some variety the other player might make you discard just one strong card instead of two weak ones, so it is 3/4 which is probably a good 6.
I think it is worthwhile to test it though and if it turns out to be too strong a simple way to nerf it , apart from pricing it at 6, would be to make it a terminal.
Your "2/4 instead of 1/3" is wrong because this card goes from the whole hand, not just the drawn cards like Advisor. This makes it weaker. Also note that they could name a weaker card instead if you happen to have a bunch of them in hand (e.g. make you discard 5 Copper instead of 1 Gold). It's letting an opponent super-Pillage you, which I think actually balances out the potentially huge draw pretty well.
If you play it from a 5 card hand and your opponent causes you to discard just 2 Copper, it's done about as well as Stables. But in most decks, you can expect that the super-Pillage effect will hurt a lot more than 2 Copper. You could try stacking Black Magic, but the card draw doesn't explode like Madman because of the built-in discard. The growth is actually not impressive at all in a low-variety deck. Even if you manage to get a huge hand, that just makes it more likely that the next discard penalty will hit multiple decent cards at once.
It's strongest in a deck with lots of variety, but those aren't trivial to build. You usually can't get a reliable engine with that kind of diversity. Even in such a deck, Menagerie may very well be better draw.
I don't know. I actually think it may turn out on the weak side.