I agree with you that from the point of view of testability both are very similar, but, in my view, from the point of view of logic reasoning are almost the opposite.
Solipsism is just bad reasoning or, at most, a semantic trick: I define my mind as everything there is out there, so, obviously, everything is in my mind. But we have science, precisely, to try to understand what it is out there, and "out there" means outside of our minds.
On the other hand, you arrive to the simulation argument by deduction. That's what, testability apart, make it interesting. The reasoning is: if a simulation is possible, then, many are possible. If there are many simulations in the universe, what is more probable? to be in the universe or in a simulation?
I agree that we don't know what to do with that, but you have to recognize that it's a damn good trick of logic.
But that is the very point of solipsism - because you are experiencing the outside world only through your senses in your mind, you are unable to decide whether the outside world even exists. The two options are 1) your body with your brain and your mind exists in the usual universe and you can learn about the universe through your senses and 2) the usual universe does not exist, only your brain or your body or something along that line actually exists and the entire universe you think exists outside of your body is just something your mind made up, your mind is simulating the universe for you.
So this is not about redefining mind to mean all the universe, it is about emptying the universe until only your body or your brain or whatever remains, dreaming or hallucinating or simulating the thing we just got rid of all day long so that you can not tell the difference.
As I have not control through introspection to my sensorial experience, surely, there is something "out there" generating it. That something is what we (or, as we are talking about solipsism, I) are trying to understand.
What is the point of saying that, what is doing it, i's "my mind"? What have we learned doing that except to mud the issue at hand?
I personally don't dream much or at least usually do not remember much or any of it, but in principle walking along a beach and dreaming about walking along a beach should feel pretty much the same until you realize you only dreamed the latter. So more or less identical experiences to you can have two very different origins, one is rooted in some external reality, the other one is just some kind of hallucination.
You can easily inspect the world of the real beach and at least in principle, maybe by lucid dreaming or something like that, you could also inspect the world of the dreamed up beach. If you never realized you were dreaming, both scenarios might be indistinguishable for you and form the reality you are living in, but nonetheless with very different underlying realities. Does that make sense? There is the reality you are experiencing (beach) and there is the reality that is causing your experience, which may (dreamed up beach) or may not (real beach) be the same thing.
In case of solipsism you experience a universe around you but there seems to be nothing you could use to decide whether you are experiencing an independent outside universe through your senses or whether your mind is just hallucinating this whole outside universe.
In case of the universe simulation you experience a universe around you but you have no a priori knowledge what a real universe and what a simulation of a universe is supposed to look like, you seem to be stuck in more or less the same place as with solipsism.
You should start to associate causation to patterns in your experience, and observe carefully that patterns. Those patterns behaviour are not decided by you, so, by definition, they are outside your mind.
I think mind is probably not the right word here because it has the connotation of control, brain might be the better choice because there are things going on you can not control (ignoring whether you actually have any control to begin with). It may have not been clear from my first comment, but I was especially referring to metaphysical solipsism, denying the existence of an independent outer reality.
Simulation argument has serious experimental issues, but I would not discard it yet. Maybe we can think of something.
Personally I just don't think about it for the moment. There is surely the possibility that we make progress one way or another, but every time I try thinking about it, it leads nowhere. Maybe one day we discover the fundamental laws of physics, logical self-consistent and the only self-consistent laws of physics possible. With mathematical proof. Do we now know that our universe is real, it is after all nothing less than the only way it could ever have been?
Or did the simulator just mess with us again? We could be using inconsistent logic all day long, writing wrong mathematical proofs and be teaching them to the next generation in our universities. But just before someone realizes the error, just after we observed the contradicting consequences of our wrong reasoning, the simulator erases the relevant memory and life goes on as if nothing happened.
Unless somebody wants you to find out, you will never find out. The potential enemy in this scenario is just so powerful, you can not win.