In this this case you have a choice. But here's some advice:

When you apply for a passport renewal, you are pretty much stuck with the USPS as you are mailing your old passport along with application to a PO Box.

So with some apprehension, last November I mailed my passport via USPS using a traceable method, complete with the tracking number. The package showed picked up at local post office and delivered to nearby USPS processing center, and that was the last update ever entered. Never showed forwarded beyond that, never showed delivered. After several days I went back to the local post office. The agent seemed unconcerned saying that happens with some frequency- that updates just don't get made. And without updates, there is no way anyone really knows where the package is.

My passport made it to its destination, but not without worry on my part.

So if you have a choice, use FedEx or UPS as I cannot imagine their being so lax about a tracking number.