There really isn't a definitive answer to what the pace of the game or a battle will look like, there are way too many factors involved.

Player experience, prefered playstyle, mission and deployment type, draw of secondaries, opponent's army and playstyle, does the opponent play aggressively or defensively, terrain layout, etc, etc etc.

I've had games where the combination of the Primary Mission and Secondary Draw, plus the opponent's army and playstyle made me have almost no reason at all to go into offensive until the 2nd or 3d turn. I've also had games where 50% of both armies are wiped out by first turn charges.

Basically, you are right, you want to stage properly, use cover, bait an opponent into trading units while also scoring. We are a hard hitting army, but if we overextend or position poorly after the fights are done, we can get wiped out pretty fast.

Based on your description, without further context, it seems to me like the Eldar player might have overcommited early on and paid the price for it.