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Okay you got a huge 12'X10' table with a central city layout (a bit more than half the real estate covered in terrain), and a 4000 point game going on.
What type of army is the most fun, and strategically intensive to play in this enviroment? A pure Assault army? A pure Shooty army? A mostly assault army with some heavy support? Or a mostly shooty army with some CC heavy infantry here and there?

I would say Dark Eldar, plenty of room to move, good cover, paper-thin armor. You'd have to have a real understanding of the army to get the most out of it before any fire power unravels them.

For city terrain, especially crowded city terrain, I always have the funnest time playing Marine on Marine games with an emphasis on Power Armor and Terminator Armor units, and with enough Heavy Support to keep everybody honest.

Probably DE yeah. 40k probably isn't the most strategically intensive game generally though.

I think you ask a difficult question, a good question. The mission played may have some bearing on the fun and strategic intensity. As you said a little more than half the real estate covered in terrain, I would imagine a fun, and strategically intense army would consist mostly of assault capable units with some ranged heavy support. The terrain if used strategically will mitigate against incoming shots.

Strategically? None. Unless you are playing a campaign of some sorts.
Tactically, DE are the most demanding. DE have almost no armour, so even a single tactical error can cost you the entire game. You have to be very careful with positioning and target priorities when playing them.

I make a motion for Tau suits and vespid army. especially stealth suits to get that 2+ cover when they do get shot at and that LoS denying second movement around a corner after you shoot. It tests the fine line between tactics and risk due to the guns they have being 18 inches. Same goes for vespids. Plus vespids get a boosted cover save in ruins. You could argue kroot too for their sniping goodness.