Do they eat up too much power? Battery discharge.

If you wire them without a relay, and they stay on with the bike switched off... they'll discharge your battery (ask me how I know).
Just don't use high wattage, and you'll be fine (55-65W). I've heard 135W+ is pushing the limits of the alternator, especially with other devices wired up.

Do they eat up too much power? Battery discharge.

I have had MINOR issues with this....

Keep the battery tendered when you're not riding, and it shouldn't be a problem....

I have'em wired only to light on low-beam.....I don't ALWAYS use'em....

I have 35w driving lights on my engine guard, I had too many flat batteries with the 55w ones, but then I use them all the time - daylight too for extra visibility. I do notice it struggling to start sometimes, but usually leaving them off for a few minutes, or preventing that by turning them off at long traffic lights - where you are stuck for several cycles, or when I'm idling for extended periods, like traffic jams, and I don't see that kind of problem.