I got a mortgage on H1-B so I don't think non-permanency is necessarily a problem. I also know several people who have gone from E3 to green card: http://www.limaechoecho.com/2012/11/e-3-visa-to-green-card.h...
H-1B is dual-intent (i.e. not non-permanent) & better known to banks (3k vs. 120k granted per year).