It's going to depend entirely on how low-resource the embedded machine is. In general terms, though, a higher-end embedded system could run a full copy of Windows or OSX on it if there was sufficient RAM and storage space available. It'd just be very slow. (Caveat: There are some embedded systems that are quite powerful, but still use embedded OSes for stability or simplicity's sake, since they don't need a full desktop OS running and/or don't have the disk space on hand for one.)
Embedded OSes usually have everything not absolutely necessary for the purpose stripped out, to minimize the amount of disk space and RAM they need, and to reduce CPU overhead so that all the available power can go to the app being run, but they're otherwise not so different from desktop OSes.
iOS is sort of an example; it's effectively a higher-end embedded OS, but the core codebase comes from MacOSX. Recent model iPods/iPhones have had 600MHz CPUs (with the performance per clock being in the general ballpark as older desktop CPUs) and 256MB RAM, 1GHz and 512MB for the current iPhone, which is very roughly equivalent to maybe a base-model iMac of the G4/lamp shade era. Running a full copy of OSX on those resources is entirely possible, but it would be slow and with 256MB RAM you wouldn't be able to run much in the way of apps, while the very-stripped-down iOS has a decent amount of RAM left over.
More pruned embedded OSes are capable of running on much, much less, of course--I've seen bragging of a fully functional OS, including a network stack, that'll fit in under 2MB of space. The one time I compared a specific application that I'd built using a system that could target very small, lightweight embedded hardware as well as full desktop OSes, the embedded version was about 1/10 the speed of the desktop one.