Where is the best place to carry water (back or bike)?
Best?  Doesn't seem like there's any one right answer.

Pros for carrying on bike:


Weight is on the bike, not you
Doesn't make your back all sweaty
No adjustments necessary
Generally easier to clean
Easier to choose alternate beverage options (with the right bottle)
Easier to just always have a water bottle on the bike (one less thing to worry about remembering to bring)


Pros for carrying in a hydration pack:


Easier to drink from (so you drink more often in little sips)
Can drink without waiting for smooth riding (don't necessarily need to remove a hand from the handlebars)
Less likely to pick up dirt (cleaner; but see comment about flip-top for bottles)


Seems like the kind of cycling you're doing makes a big difference.  Mountain biking has more dirt and more rough terrain where your water bottle nozzle could pick up trail dirt and be hard to reach down and grab to drink from.  Road biking tends to have plenty of smooth pavement allowing for drinking from a bottle and not as much dirt to worry about.

I mostly ride on the road and generally use a water bottle (or two or three; or a water bottle and a coffee travel mug), but if I'm going for a long ride (especially in hot weather), I'll use the hydration pack (and probably have a bottle in all 3 cages, maybe with juice or something like that in one) just to be sure I keep well-hydrated.