This question has run for years.
Having worked in both systems I would say that on balance the FAA flight release/dispatch system offers aircrew much more support pre-flight and in the air.
The FAA system is ingrained in history and law so US crews, or other countries that follow suit, have aircrew who know the system and where the dispatcher fits in. Importantly also, is the Aircraft Dispatcher is licenced to the same written qualification as the pilot and requires re-current training to keep him current in all related subjects. Immediately they have credibility with their pilot colleages.
ICAO Annex recommend the licencing of Flight Operations personnel but it is a recommendation not a standard, regretably the UK has never adopted this, dispite the best efforts of the British Guild of Operations Officers back in the 1970 and 80's.
We in the UK suffer, and I speak in very general terms here, from the lack of a formal accreditation in flight ops studies. Simply, we need a formal qualifcation which sets the minimum standard for all personnel exercising operational control over a commercial operation.
It has nothing to do with removing a pilots authority over the operation of an aircraft but everything to do with supporting him in flight and offering ground based information which is not readily available in the cockpit, although in a few years that will change.
The exercise of operational control in a commercial sense should never pose a risk provided you are operating within the confines of the Ops Manual, not least of which the Commander of the flight has, after all, the responsbility to say no if in his/her opinon it does.
On the question of busy flight, perhaps our pilot colleages could answer that one.