One of my lights annoys drivers and the other one nobody sees, how bright is actually right?

The part most people neglect entirely: being seen from the side.

A front light and a rear light cover you from directly ahead and directly behind. A large share of urban collisions happen at junctions, where a driver is approaching from the side and sees neither.

What helps, cheaply:

Reflective sidewalls on tyres, or spoke reflectors. Genuinely effective and passive: no batteries, always working.

Reflective material low down and moving. Ankles and pedals. Movement is what the eye picks up, and a moving reflector reads as a person on a bike rather than as an ambiguous light.

Something on the sides of your bag or jacket.

Also worth knowing about flashing versus steady: a flashing light is easier to notice and harder to judge distance and speed from. The usual compromise is one steady and one flashing at each end if you have two, or steady on unlit roads where you actually need to see, and flashing in town where being noticed matters more. Some places also have rules requiring a steady light, so worth a check.

And for the rear: a steady rear light plus a reflector is more useful than a very bright flashing one, which some drivers find genuinely disorienting at close range.

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.

The practical failures, which are more likely to affect you than the beam pattern.

Battery life is quoted at the lowest setting. A light claiming a long runtime often gives you a fraction of that on the setting you actually use. Check the figure for full output, and assume less in the cold, because batteries lose capacity in winter and that is exactly when you need them.

Charge on a schedule rather than when it gets dim, since most of these fade gradually and you will not notice until it matters.

Carry a small backup, front and rear. It does not need to be good - it needs to exist, so that a dead light is an inconvenience rather than riding home unlit. This is the single most useful thing in this thread and it costs very little.

Check the mount. Cheap rubber mounts perish and the light ends up pointing at the ground or in a hedge. This causes more failures than the electronics do.

Two rear lights is worth it if you ride a lot in the dark: one on the bike, one on the bag or helmet at a different height. Redundancy for the direction you cannot see.

And for your existing pair: keep both. The small one is your backup now, which is a job it can do well.