Lieutenant General Sir John Kiszely recently stated that "all insurgencies are sui generis," meaning that all insurgencies take place within a specific social, cultural, historical and geographic context. The implication is that just because an army might have some experience fighting one insurgency, it doesn't necessarily mean they've cracked the code on fighting all insurgencies. In Iraq, you could argue that going into the war not knowing anything about fighting insurgencies at all was preferable to going into the war thinking you know exactly how to fight an insurgency because of experience in, say, Northern Ireland. In instances, for example, where the Brits tried to "police" southern Iraq in the old imperial fashion, it didn't work out too well in the long term. And most British generals with whom Abu Muqawama has spoken seem to agree that while neither the U.S. or British military has done a perfect job learning how to fight COIN, the Americans are way out ahead in the learning process.
The bottom line is, there are lessons from each insurgency that can be applied to others. And FM 3-24 does a good job of compiling general rules and lessons that aren't rooted in one specific historical example.