kind of. But kind of not
The EMX is truly a module, it’s something you would probably design a PCB to put it on, you could hardly ever consider it something standalone. Without the extra parts that exist around the module (in a Cobra or another development board) it will function but is hard for instance to connect any external devices to. Check out image 3 and 4 in the EMX module, and if you then check out image 1 in the Cobra you can see what I mean - the little pads on EMX/3 are the parts that are soldered to the Cobra mainboard in Cobra/1.
EMX module http://www.ghielectronics.com/catalog/product/128
Cobra mainboard http://www.ghielectronics.com/catalog/product/131
The code is exactly the same - it all runs on an EMX. So you don’t have to port your code to anything. You might have to be careful about the new hardware you build, since for instance unless you add the SD card holder, you couldn’t expect the new device to support using that.
The comparison that I would make is you would either buy a Cobra or an EMX Development board, you would not buy an EMX module on its own.EMX Dev board at $300 vs Cobra at $150, plus a display and holder.
You can probably consider the Cobra as a fantastic development board, or the EMX Dev board as a different dev board that has a different set of features. In my eyes the Cobra is a fantastic platform to start on, with a great range of flexible options for things like displays and device connections. The EMX Dev is a fixed screen option.
Edit: Here’s the power info.
All these devices will work when powered via USB. Plug it into your PC and away it goes. The bigger screens though draw more power than the USB can reliably deliver, so you need to use a power-pack. The device comes with a USB cable, but not a power-pack. In the US they call them wall warts, we (in AU) just call them power-packs or plug-packs. There’s a sticky thread on optimally powering these devices - http://www.tinyclr.com/forum/10/574/. You should get a suitable power pack - electronics shops usually have something suitable, Just remember the current draw is important.