Which do you use/prefer?
I prefer to use computers, which tend to use the percentage method.
we also prefer the percentage method...
Wage bracket is the percentage method but all the computations have been done and the withholding rounded to an average for the bracket. It is a convenience for employers who do not use a computer to make the computations. It decreases the potential for computational errors when computing withholding manually. It can have the rounding "slop" in it because withholding is simply an estimate (for income tax, not FICA taxes as those are the actual taxes). Even if using a combined wage bracket table for income and FICA taxes, the slop is in the income tax and not in the FICA taxes.
For a computer, the wage bracket method would be a rather large look-up table or an additional computation to compute the wage bracket amount from the amount computed by the percentage method. The percentage method is easier to program, update, and verify. It also has fewer opportunities for programming errors or typos than the wage bracket method.
The key word is easy. Payroll is inherently hard with bad results if errors occur. You can never make your payroll process too easy. There is no acceptable error level in payroll.