Always look at the whole board

Explain in detail why Rf1 is a much better option than Qb4 in this position.

Diagnosis of the position

Before comparing the moves, it helps to see the full picture. Materially White is winning comfortably: they have two rooks, a queen, and a bishop against a rook, queen, and bishop for Black (a full extra rook, plus an extra pawn: 4 white pawns to 3 black pawns). In a "normal" position this would be trivial.

But the white king on h3 is badly exposed: there's no pawn on g2, so the king depends entirely on the pieces to cover g2, g3, and g4. And Black has exactly the battery needed to exploit this — queen on f2 and rook on f8 lined up on the f-file — with a concrete mating idea available against almost any white move that doesn't interrupt it:

...Qh4+ (opens the f-file)
Kg2 (only square)
...Rf2+ (the rook comes in via the now-open f-file)
Kg1 (only square)
...Qxh2# (mate: g2 covered by the queen, f1 covered by the rook, f2 occupied)

I checked this with Stockfish against a "passive" control move (40.Bc4, which touches neither the queen nor the f-file): the engine confirms mate in 3 with a variation of the same type (40...Rf3+ 41.Kg4 Qg2+ 42.Kh5 Qh3#). In other words, this isn't a vague threat — it's lethal, and almost any move that doesn't defuse it loses by force.

Why Qb4 loses

40.Qb4 does absolutely nothing against this mechanism. The queen goes to a seemingly active square (eyeing b6, pressuring the b-file), but it doesn't control any of the critical squares (f1, f2, g2, h4), nor does it touch the black queen. Stockfish at depth 30 confirms:

40.Qb4 Qh4+ 41.Kg2 Rf2+ 42.Kg1 Qxh2# — forced mate.

That is, Qb4 turns a winning position (+6 in material) into an immediate loss. It's not "worse" — it's losing.

Why Rf1 wins

40.Rf1 directly attacks the black queen on f2 (the rook, from b1, lines up with f2 on the f-file). This has a dual effect, and it's the key point of the move:

It forces Black to react immediately, so they don't have time to carry out Qh4+/Rf2+/Qxh2#.
It occupies/controls f1 and f2, which are precisely the squares underpinning the mating mechanism. If Black still tries 40...Qh4+, now 41.Kg2 is perfectly safe, because Rf2+ no longer works: the white rook on f1 controls f2 and would simply capture it. The engine confirms that after 40.Rf1 Qh4+ 41.Kg2, White is winning overwhelmingly (+11.8), with Black having no resources left.

The main line the engine gives is likely the one you saw in the analysis:

40.Rf1 Qxf1+ 41.Qxf1 Rxf1 42.Rc8 Rf8 43.Ra8...

Here, Black, forced, captures the rook with check, the queens are traded on f1, and the black rook recaptures. The final material result is R+B+4P (White) vs R+B+3P (Black): a technical endgame with an extra pawn, relatively straightforward to convert (which is why Stockfish evaluates it at around +0.6/+0.7 — a modest-looking number, but one that represents a cleanly won endgame, not a shaky position).

The real comparison

This isn't "Rf1 is a bit better than Qb4." It's:

Move Result (Stockfish, depth 30)
Rf1 Neutralizes the mate, forces favorable trades, won endgame (extra pawn, R+B vs R+B)
Qb4 Mate in 3 for Black

Rf1 is the move (likely the only one, or nearly so) that recognizes the real problem in the position isn't "how do I increase my material advantage?" but "how do I defuse the mating attack on my king before doing anything else?" Qb4 plays on the wrong register — it improves the queen's position without realizing the mating clock was already running.

AAAHHHHHH, IT'S BACK!!!

Isn't it interesting? An experienced player should see that black's main threat is Qh4+.

No, its not interesting... Qb4 insta-loses to an obvious mate. Why would anyone even consider it? You need to defend against the obvious mate treat. This is basic chess 101... When the opponent threatens something, act to negate it. There is nothing interesting.

The AI crap analysis is only nonsense... As one example: Why does it work? "It forces Black to react immediately, so they don't have time to carry out Qh4+/Rf2+/Qxh2#." This is complete rubbish... Time has nothing to do with it. Indeed, since the treat is a "checking-mating-attack", the only way the "doesn;t have time" argument could ever be relevant is if you played a check. Since you did not, then the time argument is simply wrong.

It works because you defend the key mating square, simple as that.

Again, the AI slop you are spreading is worse than wasting everyone time. If some weak players actually believe the crap, it will actually hamper their progress and cause more misconceptions.

From now on, I am gonna have allergies and nightmares to AI responses because of only one Lichess user...

@fernandocatolico said ^

Diagnosis of the position

The pieces must always protect the king. Why did you send them on vacation?