As far as which powers hold the advantage, the Variant win percentages for each power could be a helpful starting point.
Classic - England* vs Turkey - England 1243 (50%), Turkey 956 (39%), Draw 273 (11%)
Classic - France vs Austria - France 1319 (39%), Austria 1863 (55%), Draw 202 (6%)
Classic - Frankland vs Juggernaut - Frankland 760 (57%), Juggernaut 501 (37%), Draw 76 (6%)
Classic - Germany vs Italy - Germany 1366 (60%), Italy 821 (36%), Draw 98 (4%)
Classic - Germany vs Russia - Germany 183 (26%), Russia 480 (68%), Draw 45 (6%) (These stats seem skewed. Germany can't win 26% of the time, starting with 3 units against Russia's 4. Something else is going on. Maybe it's become standard for Russia to reveal its moves to Germany in advance? I played it that way the one time I tried this variant.)
Cold War - USSR 1447 (46.7%), NATO 1508 (48.6%), Draw 145 (4.7%)
Duo - Red 645 (46%), Green 592 (42%), Draw 161 (12%)
(Given the number of games, Red's advantage seems statistically significant, even though the two sides are mirror images of each other. Maybe Red's advantage is starting at the bottom of the board and working toward the top, as in online chess or standard board games.)
Fall of the American Empire: Civil War! - Confederacy 1208 (51%), Union 976 (41%), Draw 195 (8%)
Lepanto - Holy League 92 (39%), Ottoman Empire 91 (39%), Draw 52 (22%)
You can see the full statistics for each variant under Variants-->[Select variant]-->View statistics.