EL34 certainly has the natural mids, highs can sound a bit rolled but I found various methods to solve this. Bass was the one area I found EL34 a bit wanting, sometimes a bit soft and warm, never could get impact AND tuneful, articulate bass. Sure I could have attained better with more work and finding sympathetic partnering equipment, attempts at this ended with discovery of 845 SET. And then we come to present Frankenstein Khorns, 845 is excess, its like a brute compared to the subtlety and refinement of 300B. The EL84 PP is right up there in refinement, subtlety, natural presentation, also has extended highs, more articulate, forceful bass than EL34. Bass very similar to 300B in my setup, virtually exact same settings on volume/gain, no change in sub settings. And this with REL subs, so high level settings connect to amp binding post and chassis ground, supposedly REL's take on personality of amps to some extent. 300B sometimes gets bad rap on bass, I hear no issues and I'm a stickler for articulate, tuneful bass.
Bottom line, I can very much relate to lowtubes in regard to comparison between SET and PP, in my case this being 300B and EL84. Difference with micro dynamics is present issue, but this early days.