UPDATE April 2, 2020 - A small business can apply for both an EIDL loan and a PPP loan. The proceeds of each loan cannot be used for the same purpose. For example, if you used the proceeds of the EIDL loan to cover payroll for certain workers in April, you cannot use PPP funds for payroll for those same workers in April, although you could use PPP funds for payroll in May or for different workers in April.
If you plan on keeping your same payroll costs and same employee numbers you had before the disaster (you may also hire back employees that have been laid off to get back to the same payroll costs and employee numbers), the PPP loan makes the most sense to cover payroll costs, rent, utilities, and mortgage interest for the 8 week period beginning with PPP loan funding (these costs are eligible for loan forgiveness). An EIDL loan can then be used for other financial obligations, accounts payable, and other bills (keep in mind if you request the $10,000 advance grant option with the EIDL loan, it will reduce the amount of loan forgiveness of the PPP loan). Also, keep in mind the EIDL loan will need to be paid back.
An EIDL loan only (without a PPP loan) makes more sense if you DON'T plan on keeping the same payroll costs and same employee numbers.
The table below compares the terms of the EIDL and PPP loans: