Hello: Is the heater in a basement, or is it on the same level as the house? It could be that if it were lower, hot water could convect up the lines, giving you quicker delivery. Does the new tank have heat traps, while the old one didn’t? Heat traps save energy by keeping the hot water in the tank when no hot water is being used, but will stop convection and possibly give you the effect you are living with now.
Is there a cross connection? Go to tanklets and read up on how to test for it. That would be a coincidence, but coincidences happen 😎
Do let us know some details!