Wattage 4 or 8 ohms?

Definitely go with the output into 4.

Saving a detailed explaination for others, suffice it to say tht when I have 4 ohm speakers (speakers with a nominal impedence of 4 ohms) I assume that they have a lower minimal impedence, and I look for SS amps, of what-ever power rating, that double their power output rating at 8 ohms, i.e. 200wts at 8 ohms to 400 wts at 4 ohms, 800 wts at 2ohms. This insures that the amps has sufficient current delivery to drive difficult loads. With a tube amp I look for amps that not only have sufficient wattage but that have 4 and 2 ohm output taps.

FWIW.

There isn't a universal answer. In my case, as per the manufacturer, the power recommendations are based on the standard 8 Ohm power rating for amplifiers, but, the manufacturer assumes that one is using a high quality ss amp that "doubles down" and suggests that if one is using a tube amp they choose one(s) with increased power output to compensate for the minimal impedance load. For example if the speaker has a 4 Ohm nominal/4 Ohm minimum impedance and the suggested power requiremnets are 50-250 Watts per channel, choose an amp that can provide between 100-500 Watts per channel into 4 Ohms. In most cases that would mean a high quality ss amp that "doubles down" rated at between 50-250 Watts per channel, or a tube amp rated at between 100-500 Watts per channel. FWIW, there is an old audiophile rule of thumb that suggests that one start with doubling the manufacturers minimum power recommendation.

I drive my Thiel CS6's with a Pass Labs X350. I has a power rating at 4 ohms impedance of 700 w/ch. My speakers have a listed max power rating of 500 watts, but when talking to the manufacturer, they were ok with that.

It's all about quality and quantity.8^)