I worked in 3PL (third-party logistics) for twenty years, and our contracts used FedEx, UPS, DHL, and USPS. Most of them do a good job most of the time, so the differences largely become what happens when things go wrong. UPS is absolutely, hands-down the most useless and least responsible one. One of our contracts pulled out of UPS because Useless Parcel System totally refused to take responsibility for any problems. Boxes with tire tracks on them had claims denied because or "insufficient packaging" daily. They would claim delivery because a driver scanned the delivery even though they never stopped at the address. Local manager personally promised to hand-deliver a package that was mis-routed (and re-routed incorrectly three times) and it still went on the regular truck and was mis-delivered a fourth time.
My current company does a lot of USPS and FedEx shipping, I won't use UPS at all. Most of our USPS is Priority Mail Express International (confusing name, they have "Priority Mail" and "Priority Mail Express"). Express adds a service guarantee that simple Priority doesn't have. It works well most of the time, but it is a problem on the few occasions when it doesn't work right. But it's been pretty rare and the tracking is OK- it only updates once a day it seems, but as long as the package is scanned at each transition it's pretty accurate. Once it gets out of USPS' hand, like when it gets to an International Service Center (the ISC in Chicago is really common for our stuff) then it's in Custom's hands and USPS can't do much at all. And US Customs is almost impossible with which to work.
Dimensions are key, because there's only so much room in the truck/plane. Lots of loads cube out (get too big to physically fit) way before they weigh out (get too heavy for the vehicle) and that's what costs money. Shipping an electric bass requires a pretty good sized box to do it safely and reliably, and that's what you're paying for. How to save money and still do it right? Get a box made for shipping an electric bass- it's made to shipping standards and while oversize, it's not too big to ship normally. Pack it right to avoid damage. Set up an online account with your shipper and use it to print labels. If your choice for drop-off is a UPS store, arrange for the carrier to pick it up. Ship to business addresses rather than residential (Fed Ex's online shipping app checks that and lets you know). Residential is more expensive because it's slower- the drivers are stopping more frequently and delivering fewer packages per stop. And don't use UPS.