Two things are going on and they are both fixable without buying a third light.
First: the numbers on the box measure total output, not where it goes. A light that scatters its output everywhere and a light that puts it on the road can claim the same figure and behave completely differently. What matters is the beam pattern, whether there is a defined cut-off at the top that stops light going into oncoming eyes, or whether it is a round blob.
Round-blob lights are why cyclists get flashed at. The bright part is aimed at your face by the geometry of the design. Lights with a shaped beam put a wide pool on the road ahead and almost nothing above the horizontal, and they can be genuinely bright without annoying anybody. Some markets regulate this and lights sold there are usually shaped; elsewhere it is not required and most lights are not.
Second, and free: aim it down. A large share of dazzle is a perfectly reasonable light pointed too high. On an unlit road you want the bright part of the pool landing several metres ahead of your wheel, not at the horizon. Set it up against a wall, then check it on a dark road.
So before spending: aim the bright one properly. That alone often solves it.