Aside from specific army units, is it generally better to work on breaking your opponents force or beating up their heroes?

Magic can be a lot of combat based heroes achilles heel.

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It depends on both the scenario and your opponent's force. As much as most scenarios award VPs for both, there are a lot of factors that contribute to your decision. I found myself playing Rescue as the Attacker at the weekend, I had to kill Burdhur to win the game but could deny my opponent VPs by breaking him. Burdhur's incredibly tough so I decided to try and slaughter his orcs to break him and hope that Burhdur then ran away as he has a relatively low courage. Conversely, if I was playing an elf army in the same situation then the leader would be unlikely to fail a courage test so I would be better trying to kill him in combat. Scenario objectives also matter, to win Domination you need numbers so cutting through your opponent's normal troops is often more beneficial than going all out to kill the leader, you might well kill the leader but your opponent will likely still win the game with their normal troops.

So yeah, there's just a few examples to get you thinking, there's no right or wrong, just assess the situation at the start of each game and adapt!

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That is what i thought. I just wanted to see if there was some huge tactical error i missed in my thinking (as was the case in my original opinion regarding fate).

Apart from that you can't kill Gil-Galad in combat.
If you are against elves such as him, kill as many of their troops as you can, as otherwise, the heroes will get their pick of fights and make mincemeat of everyone.

If playing as elves, get your big heroes to kill their leader if possible. If the enemy leader is too far away, then heroic combatting is your best friend . This is pretty much all I can say as I have really only ever played as high elves.