Featured today (http://grogheads.com/?p=7716), a question about movement types....
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For strategy games, my ideal is point-to-point. Second choice is hex-based (also my first choice for computer wargames and tabletop). Tiles are generally my last choice, although I enjoy area-based movement in games like Risk and the first two Total War titles.
However, when it comes to computer war/strategy games, my *real* answer is "whatever the AI can handle best". Other concerns are secondary IMO.
War of the States: Gettysburg, 1863 from Avalanche uses regions, and the counters have to physically fit into the region in order for them to move into there.
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I've played that system and was not particularly keen on it, personally. Its what stopped me buying their 1866 game.
I much prefer hex maps, and to a lesser extent, area movement. I always feel too confined with point-to-point, but that's just me.