I was wondering the pros and cons of both of these attachments. The one I can see is that the flael mower is cheaper and will cut thick grass, were as the mulcher head can mulch bigger trees and brush better. Any info on this topic will be greatly appreciated.
I am not sure I get where your wanting to go with the question, but in my view they are two different attachments that operate at opposite ends of the spectrum with some overlap in the middle.
As mentioned the Mulcher heads are best in heavier material and in more difficult terrain. They are much more expensive to purchase and the costs can be higher depending on ground conditions. They also take a lot more machine flow and ROC to be able to effectively run a mulcher. A flail mower or rotory can be run by practically any machine due to reduced ROC and flow requirements.
The rotory mowers seem to be the lowest priced units and some make some pretty substanial claims on how large of material they can process. The flail mowers can get expensive as well, not as much as a mulcher but still can be expensive. I think they would be great for unimproved areas that may damage a rotory mower.
I have a Tushogg mulcher and will ad a rotary mower as well. The mulcher is not effective at all in grass.