I can't speak for EASA, but as far as the FAA the short version (from AC 120-76B) is that
In-flight depiction of own-ship position is classified as a major safety effect and cannot be formally authorized for use on a Class 1 or Class 2 EFB.
So basically the only kind of EFB that the FAA wants displaying own-ship position in flight is a Class 3 system (basically a permanently-installed piece of hardware that's gone through all the certification and testing requirements of any other piece of installed navigation equipment, like for example your panel-mount GPS or an approved MFD like a Garmin GMX 200).
As far as I can find the FAA hasn't given an official reason for this (I went on quite a hunt), but I suspect it is out of an overabundance of caution: Class 3 EFBs are subject to strict design and change controls (like any other TSO'd avionics hardware), whereas iDevices, android tables, laptops, and their internal/plug-in/wireless GPS receivers are not.
The FAA has no way of ensuring that changes (like say a Stratus firmware update or an iOS update) won't adversely affect the accuracy of own-ship position display, nor can they guarantee that the EFB software will correctly detect GPS errors and disable own-ship position display. They would prefer you not have the display at all than rely on possibly inaccurate information and wind up flying through airspace you shouldn't be in (or worse, flying into an obstruction) because you were trusting your EFB's position display.
A tiny bit of light at the end of the rainbow, at least for us light General Aviation piston folks:
AC 120-76B is specifically aimed at part 121, 125, 135, 91F, and 91K operators (i.e. "Not light GA").
The rest of us Part 91 folks are supposed to look at AC 91-78 (which talks about EFBs and removal of paper from the cockpit), and that Advisory Circular is blissfully silent on the subject of own-ship position.
That seems to imply that you can strap your iPad to your Cessna's yoke and turn on own-ship position display and not incur the wrath of the FAA - an interpretation you can find others on the internet agreeing with - though it should certainly not be considered a navigational reference (merely "an aid to situational awareness").
It's also worth noting that if you don't display own-ship position data there's nothing that says you can't use it -- e.g. by turning off the little airplane graphic but still centering your map based on your GPS information. I know ForeFlight has this capability.
I'm not a lawyer and I don't work for the FAA. My interpretation of regulations is worth exactly nothing.