I haven't posted on CW in a while, but I thought I'd contribute and add a much-needed Pakistan flavour to this thread. Most people's experiences of this variant of cricket will likely be different than mine as their games seem to be time-limited quick fixes rather than any prolonged game.
I've played tape-ball cricket as long as I can recall (since approximately the age of 7/8), and have loved every single moment of it - it was the first type of cricket that I was introduced to (began playing hard-ball cricket for a local club three years ago). I used to play it all day, from dawn to dusk (okay, that is an exaggeration but you comprehend my love for this variant of cricket from the statement).
We used to play with an unlimited overs rule because everybody used to get involved (all ages, from annoying children aged 6/7, to 16 year olds) and thus a limited amount of overs would never be sufficient for all of us to bat. There would also be the problem of counting the overs properly - nobody would bother doing it properly and would most likely cheat.
3 layers of electrical/insulation tape applied to the ball (with a slightly pronounced seam to emulate a 'corky' ball) produces a ball of substance, capable of generous speed/spin (and with a bounce similar to the 'corky' ball) but the main reason why I used to adopt this process was to ensure that when it hit, it hurt.
Not that I ever bowled pace (I'm an off-spin bowler, a rare type of bowling in tape-ball cricket which is usually deemed to be acceptable for a few overs when one becomes tired or a small target is required) unless dispatched for a few boundaries! And then I'd purposely aim for the batsman's head with a bouncer, helped by the fact that the tape-ball rewards bowlers who bend their back.
Playing with a relatively heavy and firm tape-ball on a cement wicket has honed my hard-ball cricket batting/bowling style (play an elegant cover drive and am equally dismissive of short balls with a nonchalant pull stroke) and I have developed a rather absurd way of bowling off-spin (basically a googly but squeezing the ball out with the use of the thumb and the index and middle finger).
Quite sad that I can't play it anymore though after becoming too old to play it (still a teenager but too old to play in the dense sort of communal square the children play in without getting dirty looks from house residents when the ball is dispatched into their gardens or something is damaged).
P.S: To answer your query on the first page, heavier tennis balls are indeed sometimes employed in India. Obviously not as good as tape-balls though. :P