And yet parcel (package) mail volume is increasing.
The funny thing is that UPS makes more money than everyone else in the package business combined,
but for rural deliveries, they (and FedEx) farm out the packages to USPS because it would cost to much to deliver it themselves.
I suppose that it largely depends on how exactly you're shipping things, what you're shipping, and where you're sending it.
In certain parts of the country, FedEx is the only way to go. In rural NE and SD, for example, I know FedEx will stop/drive by 2, 3 times a day. By 'rural' I mean anything from a couple dozen people per square mile (or less) to small towns to cities of 150-200k people.
In these places, UPS is the one that's more likely to do things like leave the packages at the local gas station (also the post office), and not bother even trying to deliver it (no wonder it's cheaper). I have had FedEx drop off several packages and then pick up at the end of the day, with the same driver. You won't get anything like that with UPS. If you want to ship something big and/or heavy, FedEx is the only way to do it with any expectation that it'll be handled well (with normal bulk rate or freight rates).
In my experience, they each excel at different things.
* UPS is good at small parcel post (letters and the like). If timeliness isn't an issue and cost is the perogative, and it's not easily broken, go for it. Most likely to read "Fragile" to mean "Step On and/or Break".
* FedEx is best at big things (eg. larger than a breadbox). They handle things the best, in my experience. If you need it timely, it'll be there, but it might also cost you. I've gotten things which couldn't have been delivered faster if someone had left for the airport to travel to me with them on a commercial flight - just ridiculously fast. It's the only way I'll ship sensitive equipment.
* USPS is the cheapest and most secure way to get something from overseas, ironically. Don't do it with anything fragile. Sometimes, you wonder if they're still using the Pony Express for some legs of the delivery.