Well, this is a complicated question :) AMD's "build more cores" strategy is, in comparison to Intel's "build more cores" strategy, all marketing. What I mean is, they both have to "build more cores" because about 10-15 years ago the strategy of building a faster single core ran into a wall known as physics. Historically, a general-purpose CPU "core" meant an equal proportion of floating-point units to integer units (amongst other hardware units, but whats important here is the ratio of one-to-one). Well, when AMD was designing their successor to the Athlon64 architecture ("Bulldozer"), they tried to predict/steer the direction of the software industry by changing the ratio to one floating-point unit to two integer units. The rational being, GPUs are essentially monstrous high-bandwidth floating-point units, so the CPU needs less FP capabilities.
But software changes slowly, very slowly, and they were either decades early or deluding themselves; take your pick. Their new architecture was both slower than Intel's "Nehalem" architecture, and less energy efficient. But changing a CPU architecture is a very expensive and highly time-consuming process, and meanwhile marketing/sales has to keep the company afloat with the cards the engineers dealt them. So to make a long story short, they changed their definition of a CPU "core" to only count the integer units, and therefore, all AMD CPUs have "double" the cores. But it's kind of a lie, because they don't control the optimization of software/compilers, which all empirically seem to work best with the one-to-one ratio.
Of course, they eventually woke up to the truth, and have been hard at work on designing a successor. That's "Zen", which you've probably heard about by now. Its head architect is the same guy who led design on the Athlon 64, and after that, took the reigns on Apple's CPU efforts (he wasn't involved in Bulldozer). But he came back for Zen, and by all rights, it should put AMD back in the fight. Whether it's a knockout punch remains to be seen. Spoiler alert: public details are light so far, but, it sounds like it's conceptually (eg at a block-diagram level) very similar to Intel's current architecture.