I am using the Android SDK Manager to install the system image for the Android M Preview. However, I noticed that there are two separate images for the x86 platform.
What are the differences between the two and which one should I select for my 64-bit Ubuntu 15.04 installation? (My CPU includes AMD-V and it is enabled in the BIOS, in case that makes any difference.)
According with this article
Android 32-bit vs 64-bit
How to run 64-bit apps on emulators
Create a new Android virtual device (AVD) based on Intel Atom processor 64-bit system image and open the AVD Manager in SDK Manager or ADT. Then click ‘create’ and fill the fields as shown in the Figure . Now the 64-bit AVD emulator is ready to run.
64-Bit Android* OS
By default, all 32-bit applications run without a glitch on 64-bit processors, but might run slower than applications tuned to run on 64-bit processors.
Android is ready for 64-bit processing
Summary
Android with 64-bit technologies for Intel Atom processor-based platforms can help developers to optimize their applications now. Building Android applications for 64-bit is just as easy as building traditional 32-bit Android applications. You can now use the official Android 64-bit emulator to run and debug 64-bit apps.
Maybe this articles can help you to understand the difference between this system images.
Update
Google now encourage to use x86 emulator like you can see in this image
The difference is that when using x86 images, it now uses fast, hardware-accelerated virtualization under the right conditions (HAXM) so it doesn't feel like there's a fat middle layer anymore.