I'm not an expert on the algorithm, but both operations achieve the same goal by creating a "mask" to scale the intensity of the sharpening. They differ on how the generate the "mask", and the arithmetic operations.

With -unsharp

Given...

For demonstration, let's break this down into channels.

Create a "mask" by applying a Gaussian blur.

Apply the gain of the inverse mask if threshold applies.

Ta-Da

With -adaptive-sharpen

Given...

For demonstration, let's break this down into channels (again).

Create "mask" by applying edge detection, and then Gaussian blur.

Apply sharpen, but scale the intensity against the above mask.

Fin

Which command will give the better results for normal outdoor images?

That depends on the subject matter. It's a good rule-of-thumb to use -adaptive-sharpen if the image contains large empty space (sky, sea, grass, &etc), or bokeh/blurred background. Else -unsharp will work just fine.