These two images show the following mold differences I found in
my supply of 2x2 round bricks:
moldsoverview.jpg:

First row:
rounded hole top, round base inside, angled side supports

Second row:
Flat hole top, round base inside, angled side supports

Third row:
Yellow bricks: flat top, straight base inside, straight side supports
TrYellow (TrNeonGreen?): flat top, straight basde inside, angled side supports

Fourth row:
flat top, straight base sides, no side support
plate 2x2 round included for comparison

support_types.jpg:
These are the three different types of side supports I found:
None, straight, angled
Apart frome these main types there are minor vasriations in the thickness of
the supports, and the size of the rectangular indentations under the studs.

Discussion:

I submit these pictures to show three things:
1. There are at least three types of inside supports on this type of brick.
2. The bottom of the brick has been made in two distinctly different fashions.
3. The top of the brick has been masde in two different styles.

The side supports probably do some little difference in the grip in
constructions where not all four of the studs are attached to the same
brick.

The straight base sides allows for more building possibilities, since
the distance between the tube and the side is a plate thickness, allowing the 
SNOT technique of attatching an old round brick to the side of a plate,
something which the newer type does not allow. 

The different top sides maght have some minor influence on the ease of 
inserting an axle or other element, but I think the major difference is esthetical.

Olof