I don't ship often, but I do receive packages quite frequently.
So from a recipient perspective, I prefer UPS for ground shipments and Fedex for express.
I say this because I despise Fedex Ground, which often uses independent third party contractors to deliver the packages. I have had quite a few bad experiences with them, and Fedex doesn't give two shits about it. UPS on the other hand has been very good for ground service. Additionally, if a package gets to the final destination facility quicker, they will deliver it quicker, even if it's before the scheduled day. I've had Fedex actually hold packages (more than twice) simply because they weren't scheduled to be delivered yet.
Express wise, while I do like UPS and Fedex, I've found that Fedex is usually a bit quicker and I've never had delays with them, which I have had occasionally with UPS overnight service.