Yes, the image is larger because you are enlarging a smaller film size more. If you put the same 300mm lens on a DSLR with a 1.6 factor and a 35mm camera, the DSLR will produce the same angle of view as a 480mm lens on the 35mm camera. And it will do it by cropping the image.
Does the enlargement end up having the same result as a longer lens? No, it does not. There is one important difference: At the same angle of view and f-stop, the DSLR will have greater depth of field.
This is hard to understand if you have always used only one film format (35mm for example), because within one frame size, depth of field seems to be related only to the f-stop and focal langth of the lens. But there are really three factors at work:
1. Depth of field increases as the lens is stopped down (the f-number increases).
2. Depth of field increases as focal length decreases (wider lenses appear to have more depth of field than longer ones telephotos).
3. Depth of field increases with the subject distance.
So... If I put the same lens (300mm) on my DSLR, I have to stand farther away from the subject to achieve the same framing, and the depth of field is greater. OR... if I insist on standing in the same place, I have to use a shorter sens on my DSLR. Again, depth of field is greater.
How important is this? it depends on the kinds of portraits you take. It's one of the reasons large-format film cameras are still preferred by many for portraits: less depth of field. (See, it works in the opposite direction, too.)
Hope this helps,