So, do your strategies vary in 1v1 games? Certainly on something as predictable as Desert Showdown, you have to adjust your play because of the very limited playing field. But on other maps...?
I find that my strategy differs very little. I grab everything I can as quickly as I can, murdering and pillaging my way through the neutrals. FFA's: Most players ask for a truce on first encounter, which I usually accept from the first player.
Probably the only difference in play is that in 1v1 it's economical to fight your enemy directly and take his cities, while in FFA's it is more economical to conserve your strength and take the neutrals first. Then if you're at the top you take the strongest you can reach down, while if you're not you take your weakest neighbor.
The whole game seems to revolve around two things: early expansion, and cash (hero offers).