For the fish obviously the best method is fishless cycling as it carrys no risk of damage to the fish.
As for speed, as said above the actual 'cycle' / growth of the bacteria will not be accelerated or slowed by having fish or not having fish in the tank.
What can make it seem quicker is for when you reach 'stable water' conditions, that of having no ammonia and no nitrIte.
Lets say you want to stock your tank to 100% of it's stocking capacity.
For arguments sake lets say a 100% stock will produce 5ppm of ammonia every 24hrs (can you see where I am going?)
So to cycle, you could add 5ppm of ammonia, only increasing it when it drops to zero, until you get perfect water.
or
You could stock with all your fish, and do many massive water changes, replace the fish as each one dies, (to keep the levels the same), and then eventually get perfect water. (Although I think this would take longer due to the frequent 'removal' of the ammonia in order to try and keep the fish alive).
Of course no-one is going to fish in cycle like that, most will start with 2 or 3 fish. Now the chances are this tank WILL cycle quicker than the 'fishless cycle', but it's a bit like comparing apples to oranges, the 2 cycles are not equal.
2 or 3 fish (purely as an example), might only be 20% of your stocking level. Based on that and that above a 100% stocking produced 5ppm ammonia, this stocking level will produce perhaps 1ppm of ammonia.
So when this 'fish-in' cycle finishes it is able to cope with
1ppm of ammonia produced in a 24 hours period, so of course it will cycle faster than a fishless cycle that is trying to process
5ppm.
I guess if you wanted to really 'under-stock' your tank then you could fishless cycle with only 1ppm of ammonia, (and I think this would probably then still be quicker than the equivalent 'fish-in' cycle due to the frequent water changes required for fish-in as mentioned previously), but what is the point, you might as well do a full fishless cycle, have some patients, and then KNOW that you will be ok for up to 100% stocking level as soon as the cycle finishes.
