Need Advice. OMD EM5 or X-E1 as FIRST SERIOUS CAMERA to learn Photography?

I think both of these two cameras have such high image quality, that one being worse than the other is rather immaterial in practice. Remember that the professional photographers just a few years ago worked with less than what E-M5 offers, and that did not prevent them from producing fabulous images. I can guarantee that E-M5 will not make you feel limited by IQ.

On the other hand, Fuji and Olympus use very different tonal curves, and it may be difficult to reproduce the other camera's look and feel, so the tonality of the images is definitely something you should seriously consider. It is not a question of better or worse, but rather of your aesthetic preferences.

The DOF control is less on E-M5, but it is sufficient for all creative purposes.

Viewfinder is another important feature that is worth considering.

I would not worry about the built-in flash - E-M5 external flash comes with a little pouch that attaches to the strap, so even if you do not keep it mounted, it is easy to always have it with you. At the same time, I think I only used it twice, and with the low light performance you probably will not want to use the flash other than to control an external flash.

For the purpose of learning both of these cameras will offer every possible control, but they follow different paradigms. Fuji uses classical film approach to camera control, and Olympus uses contemporary technologies, such as customizable control points and touch screen. Again, it is down to your personal preference.

I think that when choosing  between these cameras I would look at these features in order of importance:

ergonomics (personal preference)

selection of lenses (style preference)

accessories

image tonality (preference)

cost (compare the lenses you want and any other accessories, like flashguns)

I would not include DOF control and noise with the difference being substantially immaterial to the final print.

Vlad