2D10 is more "realistic". You get bonuses for things like massing your armor, it makes groundstrikes more powerful compared to 1D10, and the advent of an attacker result for half the units flipping means that offensives tend to peter out gradually. It's also considerably bloodier than 1D10. Terrain bonuses are more important, and raw power slightly less so.
Furthermore, it's far more deterministic. 1D10 gives you a 10% chance to crack Paris with 3 guys guarding it on a 3:2 attack, and a 10% chance for a 6:1 blitz to fall on its face with a attacker's loss and everyone flipping. 2D10, since two rolls will tend towards the mean, is much more deterministic, much more predictable.
This isn't a popular opinion, but I actually like the randomness of 1D10, I find it makes attackers in general have to be a bit more cautious about the risks they're taking. Most people prefer 2d10, IMO, because it's more predictable on the individual combat, and thus and more fitting of a grand strategy game.
I also don't like a few of the strategic consequences of 2d10. I've never once a "historical" barbarossa (M/J 41, Soviet army at the border) end in anything less than utter annihilation for the Soviets under 2D10; under 1D10, it's still bad, but not quite as horrific; and I mean the Soviets did win that war, eventually, and I think the WiF player ought to as well.
So I slightly prefer 1D10, but most people like 2D10. If there were some way to merge the tactical consideration given by 2D10 (to get you to mass your armor in the open, defend the cities, etc) with the higher stakes nature of 1D10, it'd be perfect, in my opinion.