When a player chooses an inverted rubber, they usually have a few things on their mind:
1) Is it fast or slow?
2) Does it have good control?
3) Is it spinny?
These three questions can all be generally answered by a simple physical description of the rubber.
First: The Topsheet.
The topsheet plays a large importance in the characteristics of the rubber. Firstly, is the topsheet hard or soft? A hard topsheet will give you greater speed at the cost of but lower spin. A soft topsheet will be slower, but can impart more spin. The hard topsheet will react more to incoming spin, compared to the soft sponge where incoming spin is cushioned and absorbed. This is quite often why lower and medium level players prefer to use softer rubbers. One can ignore the incoming spin to some degree and play less than perfect shot, whereas a hard topsheet forces the player to have a correct angle. To play with a harder topsheet requires a higher degree of skill, faster hands and good touch. Serves and pushing favour the softer topsheet in spin and control, yet it is possible to achieve higher spin variation with the hard topsheet, as well as shorter drop shots due to the lower contact time. Harder topsheets tend to project the ball with less arc, putting more pressure on the opposing player.
Pimple configuration:
The pimple configuration affects the spin and speed of the rubber. Generally speaking, a wider pimple produces a faster rubber. The direction and height of the pimple also dictate the spin and speed, however I don't completely understand these yet.
The sponge:
In some ways the sponge has similar characteristics of the topsheet. A hard sponge invites less contact time and higher speed, but reacts more to spin. A soft sponge lets the ball sink in for less reaction to spin, but is slower. It is possible though to get hard, dead sponges and soft bouncy sponges. The sponge can also affect the amount of spin generated, but a softer sponge does not necessarily imply more spin. For a low stroke speed, it is possible to generate higher spin out of the softer sponge. A high stroke speed gives more spin out of a harder sponge.
Back to the topsheet: Grip vs Stick
The question of grip in the topsheet comes in two forms. Sticky or grippy. I'm sure everyone has their own theory on what is better, but the sticky topsheet allows for an even higher degree of spin and control over the table. It favours topsheet only shots, such as brushing. Combined with different sponge hardnesses, sticky topsheets can play fast or slow, spinny or not. Grippy rubbers on the other hand spin less over the table with lower control and faster speed. Again, combining them with hard and soft sponges produces a variety of effects.
Sticky Topsheets and Soft Sponges:
Putting a sticky topsheet on a soft sponge doesn't always work. Over the table, the softer sponge can work in conjunction with the sticky top to produce a high overally spin. However, when the player starts to hit hard be it a loop or even a fast push, an odd effect occurs. The topsheet attempts to spin the ball, while the soft sponge attempts to cushion it. The resultant effect is the topsheet and sponge fighting each other and lower spin is produced as a result.