There are obvious dangers in trying to draw any common lessons from the fighting in Afghanistan and Iraq. First, they are very different countries and very different wars. Second, the fighting still has years in which to evolve, and each side is constantly learning from the other and adapting every aspect of their strategy and tactics. Third, these are extraordinarily complex wars are fought in different ways in different parts of each country, and where nation building is as important as armed struggle. The US and its allies must not only win in military terms, the host government must win in terms of national political accommodation, creating effective security forces and a rule of law, establishing effective governance, and creating enough development to remove the incentive to fight to live.
It is also a reality that every observer of such complex wars tends to see them the way the blind men saw the elephant: to confuse what they can sense on the basis of limited observation with the overall reality of the struggle. This is further complicated by the fact that no one can spend half a century observing such conflicts without realizing that they follow the same maxim as politics: all counterinsurgency is ultimately local. It is not enough to have the right national solution. The “edge” goes to the side that has the right regional and local solutions over time, and what works in one area may well not work in another.
That said, the attached brief does provide a survey of both wars that does imply they have common lessons. Moreover, many of the most important lessons reinforce both what the US military has learned (relearned?) about stability operations, nation building, and counter insurgency and put in Field Manuals like the one on Operations (FM-3-0), and much of the work of various study groups.