Mechanical vs electric water pump — which is better?

It depends on the use. What the dyno tests show:

• Stock 6.0 on the engine dyno (Westech): a Gen III iron truck 6.0 with its truck accessory drive (water pump, a non-charging alternator, an idler in place of the power steering pump) vs a simple electric pump. Below about 3,200 rpm there was a slight loss on the untouched stock tune; above that the electric pump pulled ahead, reaching +11 hp at 5,800 rpm, the highest speed tested.
• 2012 Camaro on the chassis dyno: swapping the mechanical pump for a Meziere electric pump went from 385 to 391 rwhp (+6). Meziere says the pump draws roughly 12 amps (about 150–160 W), a negligible load.

Electric pump pros: power above about 3,500 rpm; flow that doesn't depend on engine speed, so it will likely cool better than a mechanical pump at low speed; and it avoids the high-rpm cavitation Meziere found in stock mechanical pumps above about 6,500 rpm.

Electric pump cons: cost, and it must be a high-output unit if the car will run at sustained high speed. Meziere offers an LS version with an over-running pulley so the stock accessory drive still works.

Staying mechanical: not all LS pumps are equal. Dayco's testing (to 3,900 rpm) found the LS7 pump slightly better than the truck or LS1 pumps, and Edelbrock's pump outflowed the OE LS1 pump by about 17% while taking less power.