There are advantages and disadvantages, it's impossible to say which is better as they come out on top in different situations, i'll list these and then make suggestions where they are more suitable.
Advantages of pneumatics compared to rubber:
-Generally more power for length of a single band gun of equal length.
-Easier to load for the same power (unless you have a really long pneu and are short)
-Fully adjustable power/half power switch, whilst you can choose varying notches on a rubber gun a pneu can be analogue choice of power from 0-20/30 bar depending on model, you could have it at 8 bar for cave shooting with less damage or 30 bar with very high shaft speeds and penetration at range.
-Less snagging on weeds etc, often pneumatics are basically a tube whereas weeds can get caught between bands etc, also there is less risk of injuring your hand (watch out for the line still!)
-In many cases pneumatics are slightly more accurate than the same length average rubber gun, obviously top end rail guns are brill and prob better then pneu's however.
-Noise can be much quiter on low power settings, on high power it is often louder than a rubber gun however.
-Stealthier when moving, the tube slices cleanly through water whereas bands can chatter in the water.
-Dry barrel systems (mamba) can produce very high shaft speeds.
Advantages of rubber compared to pneumatics:
-Generally cheaper
-More simple to repair and operate
-Less likely to break down/wear and tear
-Can be transported on aircraft with less restriction due to no pressure vessel.
-Some people find it easier to shoot straight sighting along the spear, you can't do this with a pneu.
-Powerful shots can still be fairly quiet compared to full power pneumatic shots.
-There are some hideously powerful 5 band rubber guns (for tuna etc), these are prefered in this role over pneumatic.
-Can be used in sandy areas with less damage, pneu's are seriously messed up if sand gets scratches the barrel, trigger mechs on rubber are the same but can be more easily maintained, a scratched barrel on a pneu generally means a dead gun...
-Power is retained to a greater depth, only a slight decrease of power in band guns whereas at depths the power of pneu's rapidly decreases.
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-I'd say for the beginner a cheap rubber is the way to go, as the price of a starter pneu is twice or three times that of a rubber.
-If you fish in a really sandy area where fine sand is suspended get a rubber.
-If you need high penetration of big game but want a shorter gun get a pneu.
-If you have difficulty loading powerful rubber guns (my H.dessault sporasub sniper 100cm is bad!) get a shorter pneu.
-If you are mechanically minded you should be able to maintain a pneumatic if you have access to the correct 0-rings.