DHL is owned by Germany's Deutsche Post AG. They cooperate with USPS as far as carrying the parcel on U.S. soil is concerned and vice versa. USPS is slow and while DHL usually ships packages to the U.S. rather quickly, it hits snail mode once USPS handles it.
Some of these issues have to do with customs. Many imported packages have to go through it. Some logistics companies handle these procedures themselves while others just dump their shipments at the respective customs agencies at the airports, let them sort it out and assume transportation, once the stuff has been cleared.
DHL used to have their own German customs department before they cut it a few years back. Until then customs added a few hours or a day max. to foreign import delivery time. Now German customs handles it directly and they don't care about "48 hours delivery", "Express Mail" or some such premium nonsense. They take their sweet time, sometimes weeks.
These cooperating logistics carriers don't regard each other's premium services. Heard that from the horse's mouth (DHL shipping agent). Hence, when you track an international package, you usually see it take off quickly and then slow down, once it reaches its destination country.
For quicker delivery, try to find out which companies handle their own customs procedures. I think UPS and FedEx do but they make you pay for it through their tariffs. USPS is chronically slow when it comes to international shipping.
DHL is one of the most reliable and fastest shippers in Germany and within the EU, though, where customs isn't involved.