Speaking as someone who plays against eldar not with them.
I think the eldar still have a very usable codex but I wouldn't say much they have is cheesey.
Seercouncil are T3 with a 4+ not really very tougth even if they get a re-roll, and they don't have power weapons.
Holo-field falcons are hard to put down but often spend most of the game not able to shot, and hey BS3
The only thing that I get really annoyed about when playing against them is the runes of warding (think thats the one) that messes with enemy psychic powers.
I usually don't even try the powers I have as I'm more likely to hurt myself than actually cast the power, seems a little OP but eldar are the masters of the mind so
On a slightly different note my play group usually uses general all round lists not tailoring against specific armies.
With the eldar having the most specialised units I can see the possibility that some people would call cheese if the eldar army has been totally tailored against them as eldar are very good at very particular jobs.