There are no real differences between the two, algebraic indices aren't required for tournaments. Personally, I prefer no coordinates, since It's incredibly easy to know which square is which. Also having no coords means you can set the board up however, as long as a1 is dark.
chess board with indices or not
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The pros are:
If you are still learning, it makes it easier to record your moves
(Thats really all I can think of)
The cons are:
As baskeyt says, no coordinates means you can set the board up either way as long as "white is right" (or a1 is dark)
Not sure but if your opponent doesn't want the board with coordinates I think they can make you use a different one (someone correct if wrong)
I have both and after you learn you don't even look anymore.
Get one with algebraic for your first board. It will make it easier for you to learn them. You can always step up later to something plain. It's also a courtesy to other beginners that you might play. I have both now but as a complete novice I even went to an art store and got some small vinyl stick on letters and numbers for a couple of my boards. That would be a good compromise if you're not sure what to buy. You can always peel them off later; be warned though that applying them evenly may well take an hour or two if you want the job to look professional.
It's better not to have a board with rank digits and file letters. You do not want to be dependent on such being present as you will not always have the choice of equipment.
The pros don't use them and neither should you.
All relevant points covered there except when followng a PGN read out or an historic game in print, it is far easier to have the indices there than counting the squares to get to the right one, I find.
But then I am old.
It's personal preference. There are many different types of players here. Many people are casual players. They like chess and play 2-3 informal friendly games a week. Chess clock? What's that? Maybe watch videos on Youtube with interesting commentary. It's not about competition for them. It's just for fun. It's not all about playing blitz online until you pass out at 3am. And rattling off 10 move notationed openings from memory.
With all that said. I have cheap mousepad boards with notations. But the nicer more expensive wood boards I own have no notation. They also sell little stickers with numbers and letters at craft shops or Amazon. Temporary notations for when you're starting out. 
Dang this is an 8 year old thread you dug up. LOL
I guess it's all down to personal preference, lager or bitter, lamb or beef........
I prefer no notation. I started with borderless boards. I never had an issue without the notation. When I bought the silicone board recently I found myself always using the notation which is slower than just figuring out the square location in my head. When I bought the mousepad one I went with no notation. I much prefer it that way.
May 18, 2021
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#10
Beginners/novices should use the boards with rank and file marked. Especially if you intend to record chess notation for your games (required in many OTB tournaments). Once you get used to notating your games, you will be easily able to know the rank and file of each square without relying on a marked board.
BTW I only want the indices whist reading from books, it's unnecessary when playing I know.
Hi, I'm a beginner chess player and i would like to buy a chess board, i see that some have indices and some not. It might be a silly question but what is the better choice, any pros and cons for each ?
Thk you