As far as I know, nobody has done any careful measurement of power and distortion at various output levels for either the stock SEX or the 'EM7 version, with either stock or upgrade iron. My theoretical analysis shows 2.97 watts for the 6DN7 and 3.35 watts for the 6EM7, ignoring transformer losses and tube nonlinearity. On the 6DN7 version we saw (if I recall correctly) a bit over 2 watts before visible distortion (probably no more than 5% distortion) of the waveshape on an oscilloscope, driving an 8 ohm 5% resistor - so I thought we could conservatively claim 2 watts.
The 6EM7 is a bit more efficient due to the smaller plate resistance, but it is also a bit less linear. To improve linearity, the 6EM7 is operated into an 8K load, even though it is "optimum" for about 7K. That reduces its power a bit. These are the conditions for which I have quoted theoretical numbers above.
If you use a lower impedance output transformer with either tube, you will get more power and more distortion. You should be able to get around 4 watts from either tube if you use a 5K transformer, for instance. Distortion at full power will be significantly higher, probably 10% or more. It will not sound much like a Bottlehead amp, and it will be especially intolerant of speakers which have impedance dips. I will suggest that better plate chokes and output transformers would probably make this compromise more tolerable.
Our operating conditions are chosen for low distortion and reliable performance with real-world speakers rather than getting big power numbers, and our conservative specifications reflect the same philosophy.