The first column of the table on page 54 was created by taking the difference between pairs of rows from the table on page 135.
Reading the earlier table, we see that a character should gain 900 gp while transitioning from 1st to 2nd level, 1,800 gp while transitioning from 2nd to 3rd level, 2,700 gp while transitioning from 3rd to 4th level, 3,600 gp while transitioning from 4th to 5th level, and 4,000 gp while transitioning from 5th to 6th level. Adding that all up, we see that a 6th-level character should have accumulated a total of 13,000 gp by the time he has reached 6th level.
Reading the later table, we see that a 6th-level character should have 13,000 gp. That's the same result as before, except a lot easier to get because we didn't have to add it all up.
So, you can use whichever you like, and you'll get the same answer. I'd use the one on page 135, because it isn't needlessly tedious.