If you're having problems with HE it there are probably a few reasons for such.
1) You are losing control of the movement phase.
A good HE general is fantastic at movement. Some armies have vulnerable units, or invulnerable units. The HE
army is vulnerable, this means he must move his army with great precision for one mistake can end his chances of victory. I've seen games lost because they HE general gave his opponent's HBVG two turns of shooting at one unit. Which was then charged by 12 knights who broke through and into the back field. This could have been prevented by moving 9" in one turn and then 10" the next giving it only one turn of shooting which could include a misfire.
Controlling the battlefield is 10^X more times important for HE than any other army. Where warriors can brute force there way from a losing situation, Empire can cordon off vulnerable sections with overwhelming Shooting dice, HE don't provide this option. Even engaging in winning combats will result in loses to your units. So you need to bring overwhelming force into sections of the battlefield at a time.
One of the ways HE do this is the 25 slave Great Eagle. A 2500 point army can include up to 6, but you are likely to see 2-3. They are the chaff, the redirectors, the march blockers, the wheel blockers. And they are pretty good at it. They fly they have a 40mm base, and T4. They won't fade away like war hounds. The opposing general has to firmly decide to remove them. If he does this too late they may have already cost him the game. I highly recommend using cannons for shooting chariots (easy VPS, and removing combat support) first, and Eagles second, or they will cause you all sorts of harm.
2) Magic
As an Empire player like dwarves you've become accustom to having quite a few
DD. With this no longer (reliably) being the case you have to play the mind game that is the magic phase. This is where knowledge is most valuable. Knowing that Earth blood can only be cast on the wizards own unit, knowing that the unboosted version of Dwellers is only 18", and insisting
before the game that you must state you are casting boosted levels is important.
You are not going to stop everything. HE are likely to have 9-11 dice to your 4-5 dispel dice. This is where you need to break his magic phase down and accept that you are going to take some loses. Luckily most HE players play the buff/hex game. They are likely to buff and hex the same combat. If he has 9 dice and he's succesfully cast withering on 3 dice, you are fighting two units, and you know he has mindrazor. Use your dispel dice to stop withering. He may fail to cast, not get IR(letting you scroll), get IR an lose his wizard, etc. But your unit isn't getting roflstomped by s3 Spearmen
and which every addition unit (Lets say cav)
3) Combat
If you've allowed the HE player to defeat you in both previous phases this phase is a forgone conclusion. You are going to lose. He is strictly speaking better at fighting. He goes first with re-rolls + whatever buff he's forced through, and his ideal unit is fighting its choice of target.
Now if you've won the movement phase by slowing up portions of his army, to endure more shooting. Killed or re-directed his chaff, giving you local superiority, and used your own multi-turn buffs. The playing field swings in your direction.
Your troops are half to a third cheaper. Meaning you will have more troops to do the same job he has his units for. Or you will have the same amount of troops + a support unit. Casting Hammer of Sigmar on you unit of halberds will stop him from charging, period. He isn't going to kill 30 models in fact he'll probably kill around 10 (7*2 swordmasters kill 15 Statetroops or 12 swordsmen. That is the best localized killing power they can muster), meaning he's looking at having to take 25-30 s4 attacks that re-roll to hit and wound . With his maybe 14-21 T3 models, who will get at best a 6+ save. He won't charge, not without help. And that is his best unit point for point unit killer.
A horde of white lions at 480 points is a target, and while it would kill 23 Statetroops. Its an obvious shooting target. HBVG, HSRB, outriders, whatever. Every model lost is a lost attack. Two rounds of shooting make this unit not usable. Bring 500 points of your own army to beat will see this unit beat. 40 halberds, and a stank for instance, or 40 halberds and 12 GW knights.
Use your light shooting and cannons to kill his cav, and chariots (if no chariots, shoot deep units). Outriders are great at this 15 shots, will kill 2.5 Dragon princes after a first turn vangaurd. That unit is for all intents and purposes useless for deciding combats. He can't even charge the outriders at this point for fear of losing his DPs to stand and shoot.
Anyway I hope that has been helpful. HE and Warriors are the armies I've played most competitively in the last 3-5 years so I can likely answer any specific questions you may have.
