Well this latest Batman series so far are two of the best movies I have ever seen. Looking forward to the third. So therefore, I since the first two have been so great, I would not like to see Batman done as a reboot, or a continuation. Warner Bros. should end it here and NOT do it again. That's what I think. However since they don't think like that, and I have to pick, I would much rather see it as a continuation. I'm pretty sure they will not be able to top Batman Begins, so why even try to remake the origin story? Might as well just make a fourth sequel with different actors, writer, and director.
They can try to beat Batman Begins, but it's so good for me, that it will be tough for them to beat. The chances of them screwing up a sequel are far less, then screwing up a remake, that has to surpass BB.