We just replaced our water heater - basic style - and now our water pressure is lower.

Hmmm... well could be all kinds of things here. I guess we start at the beginning.. work forward. To start... it could be the shutoff that you shutoff to install the water heater... sometimes you shut a shutoff and even though it seems that you turned it on and it seemed fine... sounded like it worked fine when filling the heater... but it is not always fine (here you would need to disconnect the cold water pipe and test the shutoff by opening and closing the valve... does it have full pressure.. ) IF there is pressure there then you would next look at the nipples... cold first... did you solder fittings onto the hot/cold nipples.. If you did then you could have melted the DIP tube (plastic tube that is set into cold water inlet) and you will see a wrinkled plastic inside the nipple if this is the case (may have to actually remove nipple if it is a dielectric nipple and check to see if dip tube is in properly). IF this is not the case and all is fine at the nipples... Then I wonder... did you re-use the old fittings/piping.. Sometimes old fitting get all clogged up... dunged up.. and cause all kinds of issues... which reminds me... before you do all this stuff...check your aerators at your faucets....aerators (on end of kitchen sink faucet/lavatory faucets, etc.) clog frequently after a water heater installation.

If this does not do it for you.. let us know back here and we will try to come up with some more ideas.

If my answer was helpful please RATE MY ANSWER by clicking on the RATE THE ANSWER! Button below. Thank you.
Did you use copper pipe and fittings... did you solder pipes onto the water heater nipples..

Are you talking about hot water pressure or the whole house?

I helped a lot

Does not help at all