The USPS number does transfair however it often get's uploaded either late or the consignment number get's updated to the one used by the local transport company and the original carrier isn't informed. I've had to deal with this a few times and the 3rd party companies often refuse to give you the tracking number as you are not there customer your original shipping company is. More on reddit.com

I've used UPS and it is both fast and works well. The FedEx stores by us are inconveniently located for shipping much, so I can't speak for them but I would expect similar. If you do use third party shipping services (UPS, FedEx), you should definitely make a point to inform customers there will likely be brokerage fees in addition to duties/taxes, though. More on reddit.com

I'm in the international shipping industry. All three, UPS, FedEx and USPS are considered couriers, specifically consolidators. All three typically, but not always, "ship" (usually denotes ocean freight, hence the name ship) their international packages via air freight as their target customer is shipping roughly a 10 lb box that is 12" x 12" x 12". In order to not charge exorbitant prices to get that tiny little box overseas, they need about 100 customers shipping to the same location, or roughly thereabouts, which is why they are consolidators.

Now, the reason people's cargo is opened up going air freight as to do with U.S. Customs and TSA regulations in an effort to prevent illicit activities of all kinds and to promote safety of airplane, potential passengers and employees. Though, it doesn't always have to opened to be inspected, it's not necessarily the option of the couriers. Sometimes it is.

Back to the crushed boxes, this relates to them being consolidators. Obviously, if they are shipping 100+ packages at 10 lbs each or more and your box happens to be the one on the bottom of the heaping pile (overly simplified) then you had better have excellent packaging on it or risk damage to your goods.

Lastly, UPS and FedEx generally, not always, have their own aircraft and systems in place to ensure quality service. USPS mostly sub-contracts out their international work, causing mixed results.

To finally answer your question, you need to make sure you are comparing apples to apples. Is USPS covering customs clearance and duties, if applicable to your destination? Is insurance included? Transit times? All of these can contribute to your overall shipping costs depending on whether they have direct routes to your destination, contract negotiations for specific co-loading consolidations, do they own their own assets, etc. USPS might be cheaper for that specific route, but their aren't cheaper in every location worldwide.

TL;DR Go ahead and ship via the cheapest route, USPS in this case, and insure it! ;)

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Could be several weeks. International shipments take more time, and as well must clear customs in Sweden. More on reddit.com