Is it better to allow checkmate or resign?

I have found that many would rather surrender, but I can't really tell whether there's a rating difference when you surrender vs losing.

Your rating will decrease by the same amount, regardless of if you've been checkmated or resign.

There is no difference in rating decreasing: both count as a loss and that is it.

I think people resign too much. If there is a non stoppable checkmate coming in 1 or 2 rounds it is ok to resign. But many players resign just because they are being partially beaten, or because they have a small chance of winning. Some even resign just because they lose their queens. I had many remarkable wins in difficult situations like these and some incredible comebacks. And even if you lose, you gain experience and skills with the struggle you put in the match.

Never resign!  

False dichotomy. Incapacitate your opponent and win by default.

It's polite to resign if you notice your position is not good; you're still in your right to play things out until the end. Just be warned that, just like you are NOT forced to resign when the position is clearly lost, your opponent is also not forced to deliver the quickest mate – they may "torture" you with longer sequences of moves until they deliver mate.

If you don't think you're wasting your time playing out a dead game, go right ahead.

Just to add on to what others have said, if there's an imminent, forced mate, especially a nice one, I generally just blitz out my last few moves. If I'm just down material or in a dead lost position, I resign rather than waste both my opponent's and my own time.

Agreed. Several top GMs seem to agree too. They've allowed themselves to be mated when they missed an attack. 

Generally, I resign if the game is hopeless, but there is no immediate mate. 

If you are rated U1700, you probably don't know with certainty whether a position is truly hopeless or not. In fact, most stalemates occur when one side has a K+Q vs a lone K! 

I would not recommend novices to resign their games. However, they shouldn't drag it out as long as possible. They should play at about the same speed they played the game up to that point.

It's better to allow resignation and decline checkmate. The french term for declining checkmate is j'adoube, which means to re-adjust the pieces so you're not in checkmate anymore;)

I'm not so sure about that. Seeing GMs getting mated at all is not very common. Besides, since tournament matches are always annotated, you can always find the win by yourself – especially today, when engines will leave no tactics unturned.

Resign.Don't be that asshole who keeps on playing till mate like a little bitch.

Btw,I find it bewildering that you have played over a 1000 Blitz games and still don't know wether there is a rating difference between resigning and getting mated.

Resignation is sometimes marked as respecting your opponents skill of play when an obvious play on the board is possible and it kills your game. However, for chess amateurs, they are not too developed yet to see these lines and end up confused. That being said, there is always a possibility for error and i do feel that resignations happen too often, especially in the middle game where a lot of play is still possible, even being a piece down, as you never know when an opponent might blunder. Even the best GMs are humans after all and capable of the silliest mistakes at times.

Your ratings are worse if you drag losing games out to the bitter end...logic?  You then have less time to win other games ;)...is it better to be in a new game where you have even chances, or stay in the game where you need an opponent's blunder to come back?

Vacate, and proliferate checkmate.

I played a simul recently and made a losing blunder on one of the boards. 

After quick reflection I decided to extend my hand right away in resignation - so that I just end it and have my mind free for my other battles - rather than drag a losing game in a corner of my mind - which might influence me negatively on the other boards. 

The result? You guessed it - +15 =0 -1. 

This happened in Mexico - and I was especially happy with being able to talk IN SPANISH with each of the participants, sharing views with each about his/her game. 

In Blitz it is often worth playing on when you would resign in a regular game.  You can try for counterplay (pushing pawns, attacking the king and so on), and hone your blitz skills (playing moves that are awkward to respond to quickly).  The worst that can happen is you go down fighting.  Most players over 1500 don't resign quickly at blitz.

For regular games against a good opponent - probably bow out and don't waste each other's time.

Here White played a beautiful move and Black very nicely allowed the mate to be played out:  Ponziani Game

Here is another example. This time White sees a beautiful and unusual move [knight to the back corner] and resigns.