Remote access is a much more elegant solution, I think. Microsoft's RDP for iOS is rock solid if you are going for Windows.
Yes, local would be nice, allowing one to not rely on an internet connection, but as other have already stated, VMWare software actually does virtualisation mostly, not emulation, and their stuff works in essence because of this - on Macs using Intel processors, no real emulation is needed, just a virtualisation of separate hardware. That's not an option on an ARM processor iPad.
I ran a VirtualBox Windows 8.1 VM on my home server for a long time, used the iPad to remote into it when away from home, it was literally like having a Surface tablet AND an iPad in my hands, that's how solid the experience was. I can recommend it if you absolutely need to run Windows. Ironically, there doesn't seem to be a solution out there that achieves the same kind of seamless experience between a remote OSX Mac and an iOS iPad. Sure there are remote access apps, but they all feel like you are using an iPad to access a Mac. Microsoft's RDP makes it feel like your running Windows on your iPad. You've got to hand it to them on that, they really nailed their new RDP software.