There are lots of very nice PC sharing programs out there. I used to use Splashtop on my ipad, but then I realized I wanted a real OS, not a remote sharing application. If you dislike the limitations of iOS you should really consider a full Windows tablet, if you get an Atom powered variation you will still have the same size/thickness, battery life, etc as an ipad but with full Windows 8 at your fingertips.
Otherwise if you need to have an ipad I think Splashtop is the best program out there, although I haven't tried Logmein in a while but if I remember correctly it was quite expensive. Splashtop works nicely with the Nexus 7 as well, although the screen is a bit small.
Keep in mind that it is streaming a lot of information over the air so it will never be quite like actually having windows 8 on the tablet. Over wifi it's not bad at all, but over 4g it's kind of laggy.