Is 1U the same height in a 10-inch cabinet as it is in a 19-inch cabinet?

Yes.

A rack unit, or 1U, is 44.45mm high in both formats. The difference between 10-inch and 19-inch racks is principally their horizontal mounting format; the vertical U system remains the same.

A 4U Miniline cabinet and a 4U 19-inch cabinet therefore provide the same nominal rack height, even though their widths and equipment ecosystems are quite different.