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

At the expense of sounding like an old fart, I'd say that in the "good old day" I'd direct you toward Pentax K1000 with a 50mm lens ...

But....

As ratty already said, it is not the camera.  The camera should not impede creative process, but a camera with all the bells and whistles will not make you a better photographer.

You've already identified a couple of criteria which determine some pros and cons of specific cameras:

• sensor size for depth of field control
• lens availability. 

On-camera flash is nice to have, but is not as useful as you think (http://strobist.blogspot.com/).

Shooting style matters.  If you want to use fast-moving objects, you will need a camera with a fast AF.  If you want to shoot landscapes, you'd want a camera that has a range of wide and tilt-shift lenses available.  If you are into wildlife and sports, you'd want long zooms and fast AF.  For street photography, fast standard lenses and inconspicuous cameras are useful.  For studio photography, fast standard and mid-teles and studio flash control are needed.

There is no one camera that fits the bill here.

Shopping on the web for the camera is also not the best approach.  Go to a local photo store, and try the camera in-hand, see whether it feels right, whether you feel comfortable holding and using it.

Also, with digital do not forget the heavy "back-office" load that you will acquire.  With most advanced cameras, it is no longer enough to take the picture, you have to post-process it to get good results.  Photographs require separate adjustments for monitor display and for printing.

For starters, though, you may want to consider a camera that gives you good access to manual control, and start with a fixed-focus fast lens.   The smaller your initial kit is, the more you will learn.