I work for a MA company, if I move to NH will the percent of MA taxes I pay decrease being a nonresident?

No. The tax rate on wages is a flat 5.3% regardless of residency status. However, as a non-resident you may be entitled to fewer deductions, so it's possible your tax bill may actually go up (the rental deduction for example applies only to people who rent in MA). On the other hand, as a NH resident you would not be taxed on any non-MA source income you may have (interest, dividends, capital gains, etc).