Often, both due to airport rules and restrictions but also dense air traffic, smaller private jets are put on hold behind larger aircrafts, so you might experience a situation where your private jet might wait for a few more minutes on the air for larger airplanes to land first.
Speed-wise and around technicalities, a small aircraft is not all that different from a larger one when landing and approaching the airstrip. There are times though when the air traffic controllers ask the private jets pilots to keep their speed high even on approach and in landing to avoid congestion with larger aircraft.
In general, large airports do allow smaller private jets to approach and land with no problem apart from specifications that the pilots have to follow and they should pay attention to … not get lost inside the airport! In vast airports, small aircraft might get lost among the large number of aircraft parked and landed.
You should not worry about customs though as the process is pretty much the same with the normal flights, maybe a bit more behind the scenes because of the premium nature of the flight.