Both -NH2 and -OR groups have a -I effect on aromatic rings, since the inductive effect of the electronegative heteroatoms N/O is not electron-donating but withdrawing. However, this effect is generally weaker than the resonance effect, which is why these groups overall are considered activating/electron-donating.
Both the amino and the alkoxy substituents will donate electron density by resonance as you state in the question, and I'm inclined to believe that the NH2 would exhibit the stronger resonance effect, due to the lower electronegativity of nitrogen. You can think of this as the nitrogen being more willing to share/delocalize its electrons than oxygen.
