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I try to snap the object that is selected in the screenshot onto the object behind it, similar to the one seen on the left edge on the screenshot (from which I copied the selected object). I want it to 'align rotation', so that is selected.

object to snap with 'snap during transform' options

I then press G > Shift + Z to maintain the height. However, when i hover over the surface I want to snap it to, it flips it's rotation, seemingly by 90 degrees:

weird rotation flipping

I applied rotation to both objects beforehand. Any clues? Thanks in advance.

I use Blender 2.74.

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If you applied the rotation, then this is working as expected. Transform snapping will align the transformed object's local Z axis to the normal of the face to which the object is snapped.

To visualize where the object's local axes are, set the Transform orientation to Local in 3D view > Header:

enter image description here

Since your object's local Z is aligned to the world Z, this means that the local Z is aligned with one of the small sides of the object:

enter image description here
Note the direction of the blue arrow, which is indicating the object's local Z axis.

If you use an object with a local Z axis pointing out of the large side, then it works as desired:

enter image description here

To rotate the object's coordinates without changing the geometry, see Is there a way to rotate the origin without rotating the geometry? and Set rotation values without applying them.

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This will work on rotated objects in my addon, Mesh Align Plus (make sure there's no non-uniform scaling, though):

enter image description here

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