If I measure current, that's a good gauge of energy consumption.
Reality: It's a little more complicated than that. First, you need to measure both current and voltage simultaneously. Second, you need to account for power factor.
Why does power factor matter?
Large utility customers (typically those with 100kW+ loads) contract to buy their power based on power factor (the utility requires these big customers to do this to ensure they get paid an amount of money that truly reflects the cost of the infrastructure they need to install to service the customer). Usually the utility requires that customers maintain a power factor of 0.95 or less (this will vary depending on the contract). If a customer's power factor goes below the agreed level, the utility applies an additional charge. So - power factor has a direct effect on your energy utility bill.
What is Power Factor?
Power factor is the ratio of working power or energy (kilowatts or kW) to apparent or total power (kilovolt-amperes or kVA) delivered by the utility. It measures how effectively total delivered power is being used. A high power factor signals effective utilization of electrical power, while a low power factor indicates poor utilization of electrical power. However, this is not to be confused with energy efficiency or conservation, which applies only to energy or kW. Improving the efficiency of electrical equipment reduces energy consumption but does not improve the power factor.
What causes a low power factor?
The main contributors to low power factor are motors operated at less than full load. This often occurs in cycle processes such as saws, conveyors, compressors, grinders, etc. - where a motor must be sized for the heaviest loads. HVAC fans often have a low power factor due to running at reduced load.
So why can't you rely on clamp on current meter in this case?
To derive power factor the instantaneous product of voltage and current is required - both voltage and current must be considered simultaneously. A basic clamp on multimeter does not have this capability (although the Fluke 345 does). The best solution is to use a power logger or power quality analyzer.
For more information on measuring power, reference this Fluke application note (.pdf) »