The primary difference is motive. Littlefinger’s out for revenge, Varys is out to change the world. The Spider is an extreme utilitarian with a radical political agenda, determined to replace an exploitative elite class with his “perfect prince” and willing to do whatever it takes–whatever it takes–to get there. Ultimately, Littlefinger’s story is about very, very personal demons, even as he has a huge impact on politics; Varys is certainly driven in large part by his own past, but he’s got an ideology rather than just targets, and so he actively contributes to the political questions in the text more than almost any other character.
I think he’s going to temporarily succeed as the stars align for Team Aegon in the first half of TWOW: the Martells, the sparrows, and the Golden Company’s “friends in the Reach” (coughRandyllTarlycough) are natural allies, and as Varys notes to Kevan, the Lannister-Tyrell alliance is ready to crumble from within. But “enlightened absolute monarchy” doesn’t actually work, the immense collateral damage of the war undercuts Varys’ populist agenda, and Dany is coming for the “mummer’s dragon” with fire and blood. Varys’ project definitely appeals to me at some level, but I think GRRM’s making it clear that mutilating children to further your dream of a world in which no children are mutilated like you were is not a good model for revolutionary change.