The anthem is fine and enough power for either. You are using 1-5 watts for most listening. More power will not improve the bass.
Have you tried the room correction in the STR preamp? That has the potential to increase the bass. The STR also has sub management and I personally would just add subs and highpass them in the preamp, this will take the system to another level.
As for the 804d3 I find them lean in the bass and bright on the top end. The Sopra is a much smoother and all around better speaker. How ever the Sopra 2 is not a bass monster by any means and I also find it a bit weak without subs. But it will have more bass than the 804 and be much more balanced.
For the same money you could get the Revel 328be which is much larger and of the same caliber in sound as the Sopra, the 328be will not be lacking for bass. They are often on sale for 30% off if you look around.