Pause Based: Looks more like a battle than turn based but the pausing means it will never look as much like a battle as an action based game. Can allow for more complexity but, unless you expect the player to pause every second, it can't be as complex as a turned based game.
I´m not sure if we´re in disagreement on this or not, but the fact RTwP allows for actions to happen simultaneously can add a lot to combat´s complexity.
Attacks of opportunity and such in TB don´t really cut it in this regard, the sorta exception may be phase based variant (as in Wizardry).
Another good thing about RTwP is its flexibility/"customizability", which is actually something you hinted at in the "unless you expect the player to pause every second" part.
In games with diverse encounter difficulty (which I consider to be one of the marks of good encounter design), RTwP allows players to customize combat´s "meta-flow" on the fly. More complex an encounter is, more often they´re likely to pause and they can deal with easier encounters fast in real time (and/or let the AI resolve it) without having to wait for turns.
The system is probably more prone to exploits and maybe its biggest issue is its tendency to be more chaotic when it comes to feedback and controllability. "The chaos" can be however mitigated when the system allows players to set an automatic pause bound to a certain event.
The fact it allows for simultaneous actions while it can retain gameplay largely independent on players´ reflexes is a big plus of RTwP imo.
Baldur´s Gate 2 with Sword Coast Stratagems is a good example of a tactically pretty complex RTwP experience.
Doesn´t mean I think RTwP is inherently better than TB. All systems have its pluses and minuses, type of the game is a factor, etc.
I think the main reasons why TB is lacking in recent AA/AAA RPGs is probably its relative slowness and it fits with "modern visuals" the least.