Not necessarily. The door jamb is for the OE tires and a "typically" loaded vehicle.
Higher pressure means:
1. Center of the tire may wear more than the outsides. (Bad if that happens, since it impacts tire life.)
2. Lower rolling resistance (sidewall flex) in normal driving = slightly better fuel economy.
3. Possible harsher ride.
4. Lower tire heating during highway driving (less flex = less heat generated)
Lower pressure means:
1. Outsides may wear more than the center. (Bad if that happens, since it impacts tire life.)
2. Higher rolling resistance (sidewall flex) in normal driving = slightly worse fuel economy.
3. Possible softer ride.
4. Higher tire heating during highway driving (more flex = more heat generated)
The "sweet spot" printed on the door jamb assumes many things; the actual load range of the tires (yours may differ from factory delivery), the load in the vehicle and how it's distributed, your normal highway speed and thus level of heat generated, etc. Those assumptions may or may not be true for you.
The sidewall on the tire has printed the maximum load per-tire at the stated maximum rated inflation pressure. That's an absolute limit that should never be exceeded. The closer to that load limit you get with less inflation the higher the risk of a heat-related failure, which can be catastrophic (that's to be avoided!) I am not aware of any tire manufacturer that publishes an easily-accessible load-derating curve for their tires, and IMHO that sucks -- and you can bet there is one since HEAT is the primary issue as load rises.
In general you probably want to consider the door sticker the LOWER limit and the sidewall pressure the UPPER limit -- and an absolute. Where you run between those two points depends on many things; if you get abnormal wear patterns (center or edges wearing more than the other) you're definitely running too low or high tire pressure, but if not then the trade-offs are more complex.
I typically (for everyday driving) run my rear tires ~2psi below my fronts on most FWD vehicles as I usually have little or nothing in the trunk and nobody in the rear seats. If I'm going to be traveling somewhere with a full set of suitcases and such in the back, then I run equal pressure. I favor the higher end of the pressure scale as well but I've not run into the center of the tires wearing before the sides; if I did I would cut it back since giving up tire life for a tiny increase in MPG, never mind the likely impact on traction, is not worth it.