That's not the way they will see it. Remember you are on the clock and getting paid by UPS, if they find out that you are delivering a competitors packages while they are paying you they will absolutely consider it stealing and they would have a pretty solid case for putting you on the street. I was good friends with all the couriers on my route but I wouldn't do what you're doing.I'm going to take a guess that English is your second language.
The purpose of my post was to get a honest opinion of the situation. I wanted to get other views as I consider this a grey area. I'm not defrauding UPS, stealing or falsifying anything. I am just helping out a driver who probably is making less than minimum wage. I am just guilty of being a nice guy.
Realistically, I would never expect management to approve of me delivering a FedEx package. In the highly unlikely event that it was discovered, I would expect to be told to stop it. I would not consider this to be a cardinal sin.