Are cropped images from a full-frame sensor equal quality to full APS-C images despite the lower resolution?

If I put a DX lens on a Nikon D700, it will reduce megapixels to 5.1.

I understand that FX pixels are about 2.5 times larger than DX pixels. Would I be correct to assume that, therefore, my FX image using 5.1 megapixels will produce quality equivalent to at least a 10 megapixel image on a DX camera, all other things being equal?