6 ohm speakers with 4/8 ohm amplifier

Say your speakers are 6 ohms and your amp gives out 120wpc in 6 ohms.
So, if I am shopping for an amp for my 6 ohms speakers and care about the amp’s power rating, I should go by it is power rating at 6 ohms, correct?

I should also mention that I am just asking a technical question, not what I need/want as power or not.

It's about damping factor. The 4 ohm tap will increase the damping factor, most speakers are designed for this, better control over the woofer. However, you may not like it so as suggested try them both and see what you prefer.

Like it was suggested in the first post try both and let your ears decide which is the better of the two. No harm to your amp.

Maybe I should ask differently.

If a speaker manufacturer has the following specs; do they mean the recommended power in 8 ohms or 6 ohms?

Specs:
Impedance: 6 ohms
Recommended power: Minimum 50wpc

Watts are an abstract value, a product of volts and amps. There's no such thing as an amp that drives watts, nor is there is there such a thing as a speaker driven by watts. Speaker power and impedance ratings are just about useless for telling what kind of amp will drive them well. 

All that said, an ideal amp can drive 50 watts into a .1 ohm load with practically no voltage and gobs of current, or it can drive 50 watts into a 100 ohm load with insane voltage and practically no current. 

6 ohms or 8 ohms makes very little difference. I don't take minimum power suggestions at all seriously. I'm sitting here with speakers asking for a minimum of 50 watts and I'm driving them with a 32 watt class A amp just fine.