As a long time player of Fantasy Hero (3d6 for most checks) and a FH/D&D-ish homebrew (2d10), I can attest that the biggest changes when switching dice resolution in this manner are the changes to the "whiff factor" and effects on criticals (and auto misses). The criticals wouldn't be felt nearly so strongly in Next as currently provided, because the criticals themselves aren't that impressive. In 3E, switching to 2d10 would be a much bigger change to criticals.
However, you want to adjust the "whiff factor" globally, not tweak around the edges. That is, if PCs hit to easy compared to monsters in Next, then you want to fix that independent of any "whiff" changes caused by switching resolution methods.
So let's say that giving monsters a blanket +2 to hit is a good change for monster/PC imbalance. You want to do that whether you keep d20 or switch to 2d10. Then if you switch to 2d10, you want to examine how this changes the odds for all of the (now "balanced") characters, decide if the change is bug or feature, and then adjust as necessary.
For example, given my preferences for a relatively low "whiff" game, but still some real chance of missing, if converting the current Next to 2d10, I'd give everyone a blanket +1 to hit (in addition to whatever adjustments were made to make monsters work better).
BTW, if you don't want to do the +1 to hit, but want the adjustment, using d10+d12 is a fun little variant. And using d8+d12 is an interesting replacement for 2d10 when you want to flatten the odds on those middle numbers.