With an image like this, the best and easiest solution is probably manual exposure fusion. It's easy enough to do in any raster graphics editor (GIMP, Photoshop, etc.).

For example, here's what I managed to produce from your original images in a few minutes in GIMP:

Here are the steps I used:

1. Open both images as layers in GIMP, with the darker image (moon detail) on top.

2. Temporarily set the top layer's opacity to something like 20% and move it to align it with the bottom layer. (You'll probably also want to select Layers → Layer to Image Size afterwards.)

3. Reset the top layer's opacity and — here's the trick — give it a layer mask which is a grayscale copy of the layer itself (Layer → Mask → Add Layer Mask..., select "Grayscale copy of layer").

   This makes the top layer mostly opaque in the areas where it's reasonably exposed (i.e. in the moon itself) and transparent where it's underexposed (i.e. everywhere else). This is enough to give you an exposure-fused image, sort of, but it doesn't look very good: the moon is too dark and the surroundings too bright, so we need to tweak it a bit more.

4. Select the layer mask you just created (in the Layers dialog) and use Colors → Levels... to tweak the mask levels. Here, I left the input levels alone, and just adjusted the minimum output level to around 25 (to darken the surroundings, by making the top layer slightly opaque everywhere) and the maximum output level to around 175 (to lighten the moon face by making it somewhat transparent).

After flattening the image and exporting it as JPEG, the result is as you see above.

Ps. One remaining issue you can notice in the resulting image is that there's some Mach banding visible around the moon, especially when the image is scaled down. This is a common problem when working with images featuring subtle color gradients using 8-bit color. The ideal solution is to work in an image editor that supports a higher color depth and that is smart enough to apply dithering when exporting into an 8-bit format like JPEG. If you can start with RAW images that have a higher color depth and no JPEG compression, that's even better, but not strictly required.