Here's my 2 cents worth, as a current UPS feeder pilot: the rules are all the same, it's just a question of how well they are followed. At the mainline level, I expect UPS and Fedex pilots have very similar deadlines, and none of them are ever called on to break the law. At the feeder level, there may be a little bit of difference, because UPS outsources all their feeder action through simple charter; Fedex (I think) owns all their feeder planes, and just hires other companies to operate them. (Someone correct me if I'm wrong there.) Therefore, Fedex may have a greater influence on their feeder pilots to fly safe, whereas the management of the UPS contractors may be rumored to pressure their employees to a greater extent. Maintenance rules are all the same, but Fedex aircraft are probably equipped better than the average UPS feeder. (My company doesn't put auto-pilots, wx radar, etc in their planes) Also, all airlines have specific individuals at the FAA who are responsible for keeping that airline accountable; the system works fairly well: consistent, repeated rule-breaking will be caught and penalized before too long.
Now, that's all theory, here's the real life scenario. 1. Single pilot night freight is one of the most demanding jobs in aviation. 2. Most of the pilots in this type of operation are very young and inexperienced. (Yes, there are minimum experience requirements; most pilots get that experience doing something significantly easier, or at least different, therefore the night freight job is a big step forward.) Given those points, it's easy to see why this niche in the industry accounts for more than it's fair share of statistics. Even without breaking the rules, it's not hard to misread the approach chart in turbulence, or lose a de-ice system in icing, or lose an engine on take-off, or fall asleep...
Now to get to the point of the thread: I think very few companies or individuals within a company will knowingly pressure a pilot to fly illegally. Again, there is a system of government oversight in place, you don't get away with being stupid for long. I think most of the pressure pilots feel is all in our heads; it's our first good flying job, we haven't been with the company for very long, we feel the need to prove ourselves, we know there are a thousand other people trying to get our job and are therefore paranoid about getting fired, and we end up doing something stupid. I've been there, but I eventually got over it, and realized that the boxes really aren't worth my life and/or FAA record. Most, if not all, the stupid things I've done were of my own volition, not because the boss told me to. The airfreight industry is time-sensitive, regardless of who the customer is, but everyone understands that that there are limits, and I've rarely been asked to exceed those limits.
Freight dogs have more fun