The one on the Left. It's simple, and I like both, but the one on the left shows the relation of the game to its roots (RISK) while still showing it as an evolution, something new, not a copy. They grey background of the tiles also is what Warlight actually uses, which IMO makes it feel like it represents the game better.
In other words, the one of the right looks "Better" but it doesn't represent Warlight as well. It feels foreign to me, like it's made for a different game.
Left one looks dated, like some internal corporate accounting app :P The one on the right shows more detail (better contrast between countries and cities) and... it glows! Things that glow are always better, right?
I like the styke of the right one more, except for the fading of the waters, mainly because it looks more like a line instead of fading(it s an icon, everything is smaller on it)
I prefer a map of the whole world though.(it also gives a more "open" character, for example, if the map was of japan and the area around it, i would expect the game to be about WW2 in the pacific ocean, instead of being about war in general.
I don't know of any north-south american wars(drugs?) as example though :P )
The background gradient, selection of colours and embossing on the right don't look too professional. The left one is much more sleek. The left one might be improved by reducing the border slightly, zooming in on the world slightly, and possibly lightening the blue in the background very slightly.