Calling this a battle report is a bit much, as we didn't write down note for note what happened, but I can do the best I can here.
The setup: there are two soldiers in my unit that play more recent 40k, and they knew about Classichammer nights during home station. Well, the Lieutenant made other plans, but Sergeant Sheldon not only cleared his schedule, but he borrowed my Tyranid book and rulebook to study up and showed up with that army AND about 1,500 points of Eldar to boot. My brother met us after final formation on Saturday, and we set up two tables. Specialist Rossi, a guy in my platoon, had the evening free and was interested in learning, so we wound up pairing SGT Sheldon with my brother and SPC Rossi with me. Sheldon ran his Tyranids vs my brother's Dark Eldar, and my brother helped Rossi write a list with my Space Marines and I ran Sheldon's Eldar. Not at ALL what I would have run but I was stuck with his models.
Both tables ran the Recon mission from the main rulebook: 18" deployment zones, 24" no man's land between. Infiltrators were allowed and something else that we didn't use. Undamaged vehicles and units over half strength netted an extra 200 VP each, while damaged vehicles and units below half strength got 100 extra VP.
The Dark Eldar and Tyranid battle was not the one I fought, and maybe they can make their way on here to fill in the blanks. From what I saw, they wound up each having their left flank moving forward and crushing their opponent's right flank. Sheldon said it was a draw, Ashley said it wasn't, but he was also there to teach and have fun, so the critical analysis came later that night.
My battle, on the other hand, was a little different. I flung my Falcon with Fire Dragons and Farseer full speed against their deployment zone, daring him to respond. He didn't move towards it, send a Rhino with Tac Squad and Librarian right past, stayed still and shot a different unit with the Tac Squad on the hill right next to it, and used a Hunter Killer missile from the Vindicator to stun the Falcon. THIS was his critical error, because I had a 5 man unit of Striking Scorpions with Haywire Grenades infiltrated 18" away from him, and he moved closer so he could line up the shot with his Hunter Killer. The battle didn't sway much, and when we stopped it at the end of Turn 4, it was a tie within 3 points. However, had it gone the full 6, he wouldn't have been able to force the draw.
All in all, he did well for someone who had never even cracked open a codex, and the other guy took to it pretty well. Sheldon decided that 3rd Ed. 'Nids weren't shooty enough, so he's gonna go Eldar for 3rd, and Rossi is very interested, but hasn't come close to picking an army yet.