Not totally sure since I don’t use Elevate or Strava much, but Strava doesn’t go into much detail on their adaptations of TSS/CTL/ATL. They do use forms that use HR if you don’t have power, but I think uses power if you have it.
Per my understanding Elevate is more of a pure Trainingpeaks-style PMC with classic Coggan-based calculations.
Shooting from the hip, I’d say just pick one. And I’d pick Elevate as it’s more transparent than Strava, and goes deeper into analytics if you want to go there.
And as an aside, use the #'s as an informational tool, but not as specific instructions on when to go easy, hard, etc. It’s one of the things to consider when tracking training, but not a be-all, end-all. I think Coggan used the quote to use it as a type of description of your training, but not prescription on what to do. (Well I think he was talking more about the W/kg-by-rider-class table, but I think it also applies to the PMC chart.)