D'Addario nickels are another type of strings I really like when they're "dead" (but I absolutely detest their "clanky" tone out of the box, which needs a relatively long time to mellow out so I rarely go there).
The Pyramids... I guess you could say the tone, purely based on frequency content, gets closer to flats than most roundwounds but they will still have more midrange presence and better clarity than flats (at least if we're comparing talking about "old school" flats like GHS/LaBella). They're definitely smoother sounding than "dead" Rotos though. Rotos will always have a certain heft/aggression in the mids, no matter how "dead" they get. That's what I love about them! The Pyramids are far more "polite".
The dynamics/feel of the Pyramids will still be completely different from flats though. They have a totally different attack/sustain and overall better clarity than most flats. They're very much roundwounds, but VERY mellow sounding roundwounds. Over time they develop a fat/warm tone that doesn't get overly muddy like many "dead" roundwounds do. I love them! But it's a very different tone from "dead" Rotos. Maybe more like a warmer, fatter, more mellow variety of what you get with VERY broken-in XLs?