You can determine if the tank is the problem by connecting a garden hose to the drain that is provided on most water heaters. Before doing this, be sure to shut of the electrical supply to the heater - otherwise you can damage heating elements if an electric type or waste fuel by heating an empty tank if a gas / propane fired type.
If you get a slow flow out of this drain, it means that somewhere in the cold water supply side to / in the tank - there is a problem. Inside the tank, the cold water is delivered by a "dip tube" that distributes the cold water to the bottom in the tank. Dip tubes are used in both electric and gas / propane fueled heaters. Here's a cut away view of a typical tank:
If the tube is clogged, or there is build up, scale or debris in the supply (cold water) side of the heater, flow rates will suffer. Likewise, if there is a problem with the output of the tank, it will directly affect flow as well.
If you get a good flow rate from the drain, then the issue is going to be on the hot water output side of the heater. Again, the same build up, scale, debris issues on the hot water out put pipe will cause problems with flow. Typcial tanks do not have dip tubes for the hot water side of the tank - as taking hot water from the top of the tank is most desireable and is furthest away from the cold water that rushes in to make up the hot hot water going out.
There's nothing really in the tank itself that can cause issues with flow outside of the dip tube, and piping to and from the tank.