The difference between a semimonthly and a biweekly payroll is that the semimonthly is paid 24 times per year, and the biweekly is paid 26 times per year.
A semimonthly payroll is paid twice a month, usually on the 15th and last days of the month. If one of these pay dates falls on a weekend, the payroll is instead paid out on the preceding Friday. A biweekly payroll is paid every other week, usually on a Friday.
From an efficiency perspective, the semimonthly payroll is preferable, since there are two fewer payrolls per year to prepare. Also, it is somewhat easier to apportion salaries and wages among the correct months with the semimonthly method, since there is less need for month-end adjusting entries.
From the perspective of employee relations, the biweekly payroll is preferable, since employees become accustomed to being paid approximately twice each month, and then receive two extra "free" paychecks each year. Further, it is easier for employees to budget for cash receipts every other Friday, rather than receipts that may be accelerated or delayed by the presence of weekends and holidays.
From an organizational perspective, it is somewhat easier for the payroll staff to prepare a biweekly payroll, since processing steps always take place on the same day of each week (unless holidays interfere). When a semimonthly payroll is used, processing steps constantly shift around among different days of the week, since the pay date is not fixed on a specific day of the week.
Some organizations settle upon a combination of payrolls, using the semimonthly approach for salaried workers and a biweekly payroll for hourly employees. From an efficiency perspective, the main point is to avoid weekly payrolls in favor of either of the methods presented there, thereby cutting the total number of payrolls in half.