His best bet would be to stay in njpw mostly because he's pretty much the face of the company and he will be able to make a ton of money in Japan.
Not really. New Japan is still a very Japan centric promotion and if anybody's really the face of the company, it's probably Okada or Tanahashi as these two continue to be the go to guys when it comes to the main event picture. Tanahashi has been the John Cena of New Japan for more than a decade and Okada is someone who very much comes off like his successor. Omega's already done all he can do in the company, when you get right down to it, and I felt his time as IWGP Heavyweight Champion was underwhelming. Not that he didn't have quality matches but, and this is often a problem we see in LOTS of companies, I never remotely got the sense that Omega was "the man" in the same way as Okada or Tanahashi. Like when Savage or Hart was the WWE Champion, you always felt Hulk Hogan lurking about getting as much, or even more, attention than the champion even if what he was doing wasn't remotely as important.
Omega has said lots of times that money isn't really a big motivator for him so take that for what it's worth but when it comes to money, WWE can basically offer Omega whatever he wants and I doubt New Japan will be able to match it. Omega dropping the IWGP Heavyweight Championship after just slightly less than 6 months hints at a strong possibility he might be leaving, it's just so anti-climactic after all the time he spent chasing it and the various matches that had so many writers spraying their shorts over the last few years.
At the same time, I feel like out of the other option, he would be better off going with his friends at AEW as in WWE, he would tanked and be miserable as he wouldn't have the freedom that he would have with the other options
So if I was him, I would either stay in NJPW or go to AEW but I would stay far away from WWE.
Omega has said that he enjoys a challenge and has said, in past interviews, that he's actually intrigued when it comes to working with more restrictions placed on him as he feels it's an opportunity to challenge himself. Again, take it for what it's worth as wrestlers are consummate bullshit artists and there are times Omega sounds like a massive mark for himself. I feel that if WWE gives Omega some degree of creative control, that could do a lot to bolster their position, if they're going after him or if they've already got him. Daniel Bryan's new deal affords him what's said to be a "reasonable" degree of creative control over himself;
ALLEGEDLY, one reason Bryan wanted this was because he felt so bad for Sami Zayn after seeing some of the garbage WWE had him doing, particularly the whole thing with Bobby Lashley's "sisters" as that was beyond embarrassing.
As far as AEW goes, Omega would probably have creative freedom on a near unlimited scale and if he's more interested in possibly building something, then AEW would be his likely choice. I have little doubt AEW will try to forge a working relationship with ROH, New Japan, possibly even CMLL and Impact. Otherwise, it'll just be another indy company before too long and I don't see Cody and the Bucks settling for that, especially if they have major financial backers.
If Omega stays in New Japan, he'll be a mega star who'll probably spend the rest of his career hovering in the upper mid-card and main event spots. If he joins AEW, not a whole lot will change for him and he'll probably have even more influence considering that he's probably been the single most talked about and hyped non-WWE wrestler in the world for the past few years. If he joins WWE, it'll be a crapshoot because there's no real way of telling how Vince will use him.