Would you put FAA and Rublev aka the big haired dude in the same level. I think they are although FAA has weapons. A lot of folks don't give the match much credence but review that stats for RG FAA vs Rafa. Rafa raised his game to the sublime level especially in the final set where FAA had ONLY 3 UFES and lost the set and match. I doubt if FAA is capable of playing that type of tennis.
First off, I think we need to stop comparing the young guys to the Big Three. I'm not singling you out, because we all do it. They've collectively skewed our perception of what "greatness" looks like. Below those three are about a dozen players in the Open Era who can be categorized as "true all-time greats," and the maybe a dozen more who are "near greats." Remember that each of the Big Three now have
more Slams than Wilander, Edberg, and Becker combined (or Borg + McEnroe, if you prefer, and Novak and Rafa have the same as Sampras and Agassi combined). And that's not even getting into the guys who won 2-4 Slams, some of whom at least had periods of dominance.
Meaning, the Big Three have lapped everyone else - including Sampras. For me the question is not who the heir of the Big Three will be, because that's just unfair, but who is the next guy who will win multiple Slams and perch at the top of the rankings for an extended period of time? That's inevitable, but being the heir to the Big Three is not - and may not happen for decades to come, if ever. I'm not saying that an Alcaraz or Rune, or some guy currently playing at the Juniors level, couldn't be that guy, just that it is very unlikely, considering tennis history as a whole. We haven't seen someone with similar dominance since Rod Laver, whose prime was mostly in the 1960s. And we haven't seen anyone who could consistently play at such a high level since McEnroe, or maybe Borg (or maybe Sampras, if we ignore clay). And the Big Three were more consistent than those guys, with far greater longevity.
Or to put all of that another way, there's no shame in having a career like Courier or Hewitt, and even less so Edberg or Becker. If one of them has a run like Courier in 1991-93, then I think we start talking, but even then it should be "how great will they be? How long can they sustain this level?"
But to respond to the question, I'd put FAA on their level (Medvedev, Tsitsipas, Zverev) in terms of talent and potential, but obviously the results aren't there (yet). Whether he puts it all together remains to be seen, but I've compared him to Grigor Dimitrov a couple times recently, in terms of flashing talent that isn't translating.
I see Rublev a half or full step below those three (and potentially FAA), along with guys like Berrettini, Hurkacz, Ruud, Fritz, etc. Guys who are unlikely to win Slams, but should be able to win a Masters or two, if the stars align (and Hurkacz already has), or maybe be a one-Slam wonder if they can thread the needle.
In a way, FAA is in his own category in that he's still got a wide range of possible outcomes, anything from another Grigor Dimitrov to being the third wheel with Alcaraz and Rune for the next decade. I think we'll have a better sense of his career by the end of this year. Sinner, too. Both are teetering. I like FAA's package of talent more than Sinner, who comes across a bit "soft" in my mind, without the weapons to be a truly dominant player. But as others have mentioned, I question FAA's mental game, and that's really the deciding factor on how talent actualizes itself (see, "Nalbandian, David" or "Safin, Marat").