So given Moore's law you will eventually end up with a single physical universe and hugely many simulated universes.
Moore's law is an observation about how fast technology is developing, not an incontrovertible law of physics. It will not hold forever, because eventually we will run up against physical limits preventing us from cramming more computing power into a given region.
In particular, it is impossible for a given amount of matter to perfectly simulate more matter than itself. If it were possible -- if you could e.g. use a ten kilogram computer to simulate twenty kilograms of matter -- then your ten kilogram computer could simulate two of itself, doubling its storage. Further, each of those computers could then simulate two more, and so forth, leading to an obvious contradiction (infinite storage requires infinite entropy, which has been proved impossible). Note that this argument holds even if the simulation is slower than real time; no matter how long it takes to simulate, you can't store more memory than you had to start with.
Now, of course this all hinges on the word "perfectly". There's no reason a computer can't simulate large amounts of matter with less-than-perfect fidelity, which is something that we do all the time. But given that we can build working computers, nuclear reactors, particle accelerators, and all that, let alone the vastly-more-complicated processes going on in each and every cell in your body, we are clearly not living in some cut-rate simulation which is hand-waving the laws of physics. We don't know how to model all of this stuff in a computer, but given that it takes supercomputers to simulate hydrogen atoms accurately, and we can't even solve the equations by the time we get to helium, it seems safe to assume that no matter how sophisticated our technology becomes, it will always require a couple orders of magnitude more matter than what you're trying to simulate (if you doubt this, consider a practical example of a computer trying to simulate itself. Can you really picture a computer with 4GB of memory accurately simulating the behavior of 4GB of RAM at the subatomic level? It can't even emulate a different computer with 4GB of memory, let alone simulate it at the subatomic level). So, we're talking about a computer which is, at an absolute minimum, a couple of orders of magnitude bigger than the entire universe.
(For completeness, I will point out two possible "outs" for this problem: First, it's possible that there's some trickiness going on, and "the entire universe" isn't actually modeled. Maybe only a small portion of the universe is modeled accurately, and everything else is an easy low-grade simulation used to trick us. That's certainly possible, but it's also unfalsifiable, so I'm not sure it's worth seriously debating. Second, this assumes that the simulator and the simulation are operating under the same laws of physics. If the "real world" which is simulating our world has different laws of physics, which allow for vastly more powerful computers than anything we could possible hope to build using our cheap low-grade physics, this scenario wouldn't be as ridiculous. And, really, quantum mechanics is so weird that "it was outsourced to the lowest bidder" may actually be a decent explanation for it.)
Regardless, though, I don't understand how the "it is much more likely that we exist in a simulated universe" idea is getting serious traction. No, it's not impossible, but "likely" is a hell of a stretch.