UPS is about the best in my area, none others compare, as for the postal service...........................unless its not valuable and your in no hurry to ever see if, if can live without ever seeing it might be better yet, only then maybe I'd ship through them, but keeping in mind, it took them over six years to get a letter to me that was mailed from the same town I live in and quite a few times, many things never did show up, as in ever yet, but then again, six years have not yet been up on those letters, so there is hope yet I may actually see them yet. As for parts being sent through the mail.....................................good luck with that.
Freight shippers....................boy it might be quicker and cheaper just to drive and go get the parts myself. Just got bottom excavator rollers shipped to me this past week, luckily I unloaded them myself and counted them before I signed anything, turns out someone dumped the pallet over and the driver had to move everything in the truck to find the last roller under another pallet. I was actually shocked he found it, quite a few times they can't and I get to reject the shipment completely and have the seller send via another shipper. I'm not sure how to rate most of the freight shippers, some can't find my place at all, even after driving by my yard 20 times a week and have done so for decades, some forget to call when I'm needed to sign and pick pallets off the truck and have to reschedule many times so I can be around to take the shipment. A few can't seem to keep track of any of my shipments, as in they lose them somewhere in their system, others still can't seem to ever get anything complete, as in parts are missing or lost and a few have put the wrong tag on the wrong customers parts, as in my name and address are right but I have clue as what the parts are who should have gotten them and who might have gotten mine by mistake. One shipper in particular seems to only hire the most stupid incompetent drivers, one who I hate with a passion, won't deliver anything to anyone after a certain time of day, he takes all his deliveries he has left and logs them in as delivered or address can't be found and then tosses the shipments into a box to be sent back to a major sorting center, states away and then throws away the paperwork, he's done this to many in my area, times over and yet he still has a job, the only thing I can think of is he's got to married to the boss's daughter or something equally stupid to keep his job.
To answer the question of shipping overnight and not getting it, I used to ship overnight all the time, but I knew the guys who flew the shipments in, as in the pilots, and when I shipped overnight, I'd call them directly to make sure my parts were on board and I had no issues, when they retired I've never since shipped overnight anything from anyone, doubt I'd ever see it even days later, that is a total scam in my opinion.
There are certain shippers I tell anyone shipping anything to me, they absolutely can't use them as shippers or I'll cancel the order. If I pay with a credit card, with express shipping, I have already cancelled the transaction when the parts didn't show up on time, with a credit card you can protest the charge for up to 45 days, something that is very handy when problems come up and usually gets someone's attention much faster than just calling with a complaint, trust me on this, it does work, but doubt you can ever order parts through them again with a credit card, just as a heads up, but you can threaten to cancel the transaction before actually doing it, this helps to get much faster response than just calling in a complaint of the parts not showing up on time.
As for the free shipping on eBay and such internet places, it depends, I've used this option many times with mixed results, sometimes we get things fast, other times it can take months to get things via free shipping, I always ask about a specific shipping date and receiving date in writing, that helps greatly to get the stuff in a timely manner.