I ve played severall matches against HE. What i ve noticed is :
All Mages know Drain Magic spell. This spell increases the casting value of the all spells casted after that. HE spells are affected too so its reasonable that its gonna be the last spell casted in their Magic Phase. Dont let it pass. Keep your dispel scroll or at least have some dispel dice so you can deal with it cause its very annoying.
I would suggest you try kill the mages 1st if you can. They have T3 as all elves have and most important they cant wear any kind of armour. They might have some protection though through other magic items. If you manage to kill some of the mages your life will get a lot easier. They have items that gives them extra PD and DD making their magic phase very powerfull and their opponents cursing cause they cant cast their spells
Their most frightening and dangerous unit is (drum..drum!!) The Sword Masters. ASF with great weapons 2 attacks (3 for the champion) and I 5 means they will hit 1st most of the times and deal heavy dmg (they re-roll to hit too!).The only who can hit them before they hit you are your vampires. Dont ever throw your hard hitting units (GG, Vargulf, or anything else you have) to their front, as they wont survive the round. Usually the sword masters have a BSB in them holding Battle Banner which adds +D6 to their CR (I rly hate this standard

) or (less often) Banner of the World Dragon which makes the unit immune to Magic. The way to deal with them is 1) not always effective but can help, try to reduce their number as much as you can with some magic missiles or any other kind of magic range attack. 2) the way i prefer is to hold them in one spot using ethereal creatures. Ethereals are perfect when playing against HE, cause they dont have many magical attacks and also you can disrupt their movement so they dont out maneuver you and hit your flank or rear. Wraiths and Banshee are a very good Rare option as long as there isnt a hero in them (usually there is

) or they dont have Battle Banner. Even then you could probablly kill some and win the combat. Dont expect them to flee easilly, they all have very high Ld.
As i mentioned the only who can hit before elves are your vampires so what you can do in order to beat them in CR is challenge their hero or champion, be carefull about the Hero cause he might have some dirty tricks too.
Other dangerous units are: White Lions of Chrace.They have wood strider special rule so no penalty when passing from forests, they also have killing blow and great weapons. Phoenix Guards. They are the most "deffensive" elves with a 4+ ward save, heavy armour but still T3. They can hurt you when they attack too with their halberds (ASF and I 6!). They also cause fear so the small help that our less scary units offer is lost when facing them.
Thats all i have in mind right now,sure they are more, like their dragons and their bolt throwers, but i already wrote a lot i am sorry about that
