My dryer plug is different from my outlet. The outlet is labeled NEMA 14-304 and I think my dryer plug is NEMA 10-30P. (at least that's what the configuration looks like).the dryer sticker says 120/240V 28A 60Hz 3 or 4 wire connection. Two questions - 1) can my wiring support that dryer and 2) should I change the pigtail on the dryer or the outlet on the wall?

New construction or remodeling going to 4 wire Plug and receptacle.
The 4 wire setup has a separate neutral and ground.
You can change cord to 3 wires.
There is a strap that connects the center terminal on dryer to the metal case, about 3" long, this needs to be in place for 3 wire, or removed for 4 wire setup.