I expect that cost effectiveness depends very much on size/weight. A single stamp, or a set, which fits in a regular sized envelope (basically, First Class Mail) can't have Fed-Ex or UPS be competitive, and I expect that non-competitiveness goes up to a certain weight. If it is valuable and you need tracking, then any of the services 1 or 2 day service is competitive with USPS 1 or 2 day signature-required service. Once you get above a few pounds, though, I think all services are competitive. At Christmas, I go to a MailBoxes USA to ship my packages - their lines are shorter than at the USPS and they offer many more options. Yeah, there's a service fee, but it is worth it to me. Anyway, when they put up the package and show me their screen, it shows pricing for USPS, UPS, FedEx, and probably DHL - they are all within a dollar or two of each other for ground, 2-day, and overnight. Well, for ground, anyway - that's the only service I would consider for 10-15 pounds of Christmas presents.
When I am buying small stuff online (a stamp or two, or a small set) and see a shipping fee of $1 or so, I assume it is going by USPS First Class Mail (basically, it is going in an envelope with a couple of stamps for postage). I know it will take anywhere from a couple of days to weeks to get to me. I am good with that. I am still waiting for a small lot (single stamp) to get to me from South Africa from last November. I am beginning to think it really won't get here.
Slow mail sucks!!! No doubt. I think we are seeing the slow-mo implosion of the USPS. Problem is, we still need to use them for so many things. Where cost effective, though, I would rather use one of the other guys.