I can’t really say which method is better but, do you mind if I ask where I can find those sites that do guess move?
Guess The Move vs Annotated Game Books - What is better?

Fast: book,
in the one without explanation, we do think and calculate variations as to why they played so our calculating power would increase, I think =)

There are a few different ones that have slightly different features and names but all share the same essence.
- Chess.com has some "Play Like [Name of Grandmaster]" lessons where the challenges have you playing the moves. This is typically the best section of the game rather than the entire game
- Lucas Chess has a Play Like a Grandmaster feature. It has games by Capablanca, Carlsen, Fischer, Nepomniatchi, Polgar, Muzychuk and Tal
- Chess Tempo has Guess The Move. It score each move you make and gives you full marks if you play the top engine move even if it was different from what the master played.
- I think Chessable has something, maybe it is a Pro feature, not sure.

There are a few different ones that have slightly different features and names but all share the same essence.
- Chess.com has some "Play Like [Name of Grandmaster]" lessons where the challenges have you playing the moves. This is typically the best section of the game rather than the entire game
- Lucas Chess has a Play Like a Grandmaster feature. It has games by Capablanca, Carlsen, Fischer, Nepomniatchi, Polgar, Muzychuk and Tal
- Chess Tempo has Guess The Move. It score each move you make and gives you full marks if you play the top engine move even if it was different from what the master played.
- I think Chessable has something, maybe it is a Pro feature, not sure.
Thanks

I use the Explorer. It’s quick and practical.
I enjoy emulating the few lines that I do play and gain knowledge in middle game planning.
For me, it’s about the themes, concepts and critical moves not the move by move sequence.

All of the above examples and sources are great.
Here are a two more:
1. Design your own! I've heard the following as an exercise: take a random master level tournament, pick a number in the 20's, look at that position, and guess the next move.
2. Pandolfini has a monthly column in Chess Life called "Chess Solitaire". Bonus: he gives 1-3 sentence explanation of pretty much each move. A whole bunch of them were collected and made into a book
But the OP asked: "Which study method is more effective for fast improvement?". I'm going to argue that you need both. But for improving novices (say 1000-1400 range), if I had to pick one, I'd go with annotated game collections, such as Logical Chess. After that book, McDonald, Chess: The Art of Logical Thinking. (Both books have about 30 games in them).
The idea (according to Heisman) is to spend 20-40 minutes per game, and go through a ton of them. You'll start picking up common themes as well as get diverse opinions. The problem with some of the "guess the move" scenarios -- is that you might cover only 1, 2, or 3 positions in 20 minutes. That kind of deep thought is certainly necessary, but for the improving novice, I suspect it's more important to get a general "gestalt" of chess, and thus better to go over say, two full games in an hour, rather than study 3-4 positions in an hour.

I combine the two methods to some extent, when I go over master games and the position looks critical or interesting (often you are tipped off by the timely appearance of a diagram), I try to guess the next move.

If i just do guess the move you may miss some of this.

The nice thing about the play like [GM] lessons on chess.com is you get some explanation on why moves are good or bad and sometimes go over alternative lines to see why a move would still have worked if the other player made a different move.
They are a sort of hybrid between the chess tempo/Lucas Chess idea and the annotated game books.
#1
The answer is: both! Use annotated grandmaster games, cover up the annotations and try to find your move in that position. Then look at the move and the annotation.

#1
The answer is: both! Use annotated grandmaster games, cover up the annotations and try to find your move in that position. Then look at the move and the annotation.
I think that is the key to being able to recall the correct moves, later; to make the move yourself and then see whether it is correct.
As an example, I read the Winning Chess Strategies book passively, because at the time I was away at the time without a board or electronic board. Then about 3 months later I noticed there is a lesson based on the book (on another chess training site) and tried it out and found I remembered that the game was in the book but did not remember any of the moves from the games. However, after making the wrong moves, seeing the correct moves along with the explanations, and then making those same moves myself, I am understanding the ideas a lot better.
If you need help, please contact our Help and Support team.
When it comes to studying master games, the traditional way to study is buying a book of master games (or master vs amateur games) and reading through it and playing along, typically on a real board or alternatively on an electronic board.
In recent years there are a few different apps/site that offer a Guess The Move feature where you play as one side of the board and try to guess the moves that the master made in the game. This is more interactive, but you don't get the explanations on why the master player made that particular move.
Which study method is more effective for fast improvement?