Your eye plus the corrective lens (whether on the surface, or some distance away) makes an "effective" lens with a focal length that depends on the distance between the eye and the lens.
When you are using contact lenses, that distance is fixed; when you have glasses, that distance is variable (by sliding the glasses towards the tip of the nose, or closer to your eyes).
Now typically the effect of glasses gets stronger as the lenses slide towards the tip of your nose: if you have positive diopter lenses (because you are far-sighted), you can see things closer up by sliding the lens further away; if you have negative diopter lenses (as you state), then pushing the lens closer will help.
Your optician selected lenses that had a certain curvature, expecting that they would give appropriate correction at a particular distance from the eye; but your glasses are working better than the contacts when you are looking close up, which tells me that you probably push your glasses a little closer to the eye than the optician was expecting.
You can experiment with this and let us know - does sliding the glasses towards the tip of your nose make it harder to read close-up?
The equation describing the effect (assuming two thin lenses with focal length $f_1$, $f_2$ and separated by a small distance $d$) is the Back Focal Length