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

If anything, it is easier to shoot in M mode with either camera these days because the "WYSIWYG" approach of constant liveview has given us the tools necessary to master exposure without guesstimating or taking some perverse pleasure in masochistic trial-and-error.  So far, 1950 of my first 2000 shots with the OMD have been in M mode.

Like you said, the zippiness of the OMD can help you get the shot.  Whats more - and this is coming from a DSLR background - the touch-screen with tilt is a transformative feature for people pics.  You can now take the camera into extreme angles, out-stretched one handed, and get a perfectly focused image with short DOF (thanks 25/1.4, 45/1.8, 75/1.8) pressing your thumb on the screen - instantly.  Wear a neck strap long, tilt the screen up, and shoot navel-gazing at the OLED; you are transported back to the twin-lens-reflex days! Add a fisheye or UWA to the mix, face-detect AF routines, and a whole different process to photography is possible.  If you do candids, street, ect, this effectively doubles the techniques you can use to approach a shot.

I would be right at home with the Fuji, and there is a 1-stop advantage in DOF control.  The OMD is a much better all-a-rounder however and will get you more shots... with features that point to the future of photography.

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-CW