Try removing the aerator from the faucets to see if the aerator screen has an accumulation of debris blocking it. Some debris may come through the city water supply hose if you do not use an external filter and the water heater creates mineral scale as it heats the water. Either can plug up these screens when it gets in the water lines. If the faucets are partially blocked odds are the shower head is too. If you can't take the shower head apart to clean it, try removing it and soaking it in vinegar for a few days, then flush it out.
If debris is not the problem, you could have a deteriorated rubber washer on the shutoff valve partially blocking the valve opening. This washer can be replaced by removing the valve stem. If pressure is different on hot or cold, this could be either the main shutoff valve or the valve at the hot water tank.
I have had both of these issues over the years in different 1970's trailers.
If it is not debris in the aerator screen or shutoff valves, it could be the pressure regulator. Some of the pressure regulators have filter screens just in front of them inline which can be cleaned.
If you do not find debris in these screens, keep in mind pressure regulators can fail too.