I've got more Nixon content planned
What would Hoover have to gain from doing so? Embarrassing the government isn't exactly going to help him get his job back, and a bit of petty revenge isn't worth the retribution it would invite (and Hoover can be absolutely sure that Mac isn't bluffing in his threats to destroy Hoover either... he's got a reputation for clearing anyone who stands in his way out of his government, and he's pretty much singlehandedly responsible for bringing Harry Truman down). Plus, Mac is pretty much untouchable politically - he's not running again (though Hoover doesn't know that for sure), and a substantial wing in Congress practically worship him (and if Hoover starts trying to 'scorch the earth' with his files, that's only going to put more Congressmen on Mac's side).
And Dewey's going to make sure that any files in the FBI aren't allowed to leave and get back to Hoover, so there's a bit of a limit on what Hoover could do even if he wanted to.
So, not to say that it is impossible that Hoover would release the files out of spite, but there's some good reasons why he wouldn't.
As for Mac's Philippine payment, I'm fairly sure that, while it was extremely scummy by Mac, it was technically legal.
Is he really a more admirable person though?
Who is public opinion going to side with? The war hero and extremely popular President, who probably also ranked #1 in Gallup's "most admired man" poll six or seven times* by now? Or the guy that runs the closest thing America had to the Gestapo?
(*= OTL Mac won this in '46, '47, and '51, and almost every other year it was the sitting President who won, so we can safely add '52, '53 and '54. Possibly '50 as well for his victories in Korea).
I don't think it is really feasible that absolutely nothing gets out - there's too many people involved once Dewey turns the matter over to Congress, and Hoover is much too high profile to just disappear unnoticed. What seems more reasonable is that Dewey says something in the papers to the effect of "we've found a bunch of papers proving that Hoover was spying on American citizens without authorisation, and those documents are going to be destroyed" without necessarily stating that most of the government is included in that group of 'American citizens'. If the scandal blew up any more than that, destroying the documents probably becomes a case of 'Ford pardoning Nixon' - not a choice Dewey wants to have to make, but one he does so the country can move on.
(Speaking of which, Ford is probably one of my top 5 or so Presidents, so I'm going to grant him his wish of one day becoming Speaker of the House ITTL)
- BNC