In the perfect world the two items would not be competing for the same pool of money. Each has it's valuable function and serves a good purpose. Each specific case should be determined on it's own merit or worth, and the best option available should be given preference for each situation.
It is important to provide training and education to volunteers who have actually committed to the relief so that they are better equipped to handle the situation. Spreading money to peripheral disaster relief efforts, whom may not be fully engaged in a relief or not well known to the people who need their service, may end up causing more problems because people will fear using their services and their staff may not be able to handle the disaster.
I do believe that it would be better to spend less money on peripheral disaster relief efforts and spend more money on training for the volunteers. It is more about quality than quantity. The more the volunteers are trained the more they will be able to help. They will also be safer.
No, less money should not flow into peripheral disaster relief efforts in favor of additional training and refining for the service volunteers who will actually commit to the relief, because peripheral relief efforts are the most effective. To train service volunteers would not be as effective, because in the event of an actual emergency, they would be hard to mobilize. Relief efforts happen quickly, and need to be flexible.
I don't think peripheral money flow into disaster relief efforts is the big concern for disaster striking; it's the presence of trained staff and the presence of volunteers. Some of that money could easily be funneled into a small little compensatory package (very small) for volunteers on the scene or used to help pass a law that would implement a tax break for people who receive proof (via a stamped paper or signed document) who volunteer. The real issue is not having enough immediately available resources and trained professionals and that does not go back to peripheral spending; it goes back to businesses being prepared to donate and getting those same tax incentives and job incentives for nurses and doctors as well as first responders being at an all-time low. The costs of training and schooling has increased exponentially while the interest on student loans, amounts of financial aid available, and the benefits and pay for even doctors (particularly those that are not specialists in a field as that is what most medical students are pressured to do) are at an all time low as well. If we changed our education system for medical students, implemented more meaningful changes for tax breaks for volunteers and businesses, and made sure that the peripheral funds were all accounted for, then disasters would have less of a burdensome outcome drawn out over years. The peripheral funds themselves are necessary and more important to have on hand for disaster relief organizations because, after all, we will always have doctors, nurses, businesses willing to donate, and volunteers even if motivations are low.