Does using a small base die affect chamber pressure since it sizes the case smaller?
Do you use the same recipe (ie, grains of powder) that you would use for regular dies?
1) No. Regardless of starting point the brass will swell up to fill the chamber. Then cartridge thickness and chamber internal dimensions affect pressure.
2) Yes. Absolutely no change.
Folks who claim small base dies are a gimmick just do not have the gages. I have chamber gages, cut by the reamers that cut my rifle chambers. I will drop sized cases into these gages, and with certain combinations of rifle, standard sizing die, I can observe an interference fit when a case is not sized sufficiently.
I would use small base dies for everything, if I could find them. I use a Redding T-7 press, it has plenty of leverage to small base die 30-06, 308, and .223. I small base these calibers because of the multiple target rifles in these calibers. It increases ammunition interchangeability.
The amount of force it takes to small base a 308 or a 30-06 is considerably more than if using a regular die. I have found proper choice of lubes makes a big difference, Imperial Sizing wax, or RCBS water soluble really helps. The .223 round takes very little force to resize whether standard sizing die or small base.
Since I have target rifles barreled quite frequently, it is always interesting to talk to the gunsmiths who rebarrel lots of rifles. One of the most frequent customer problems they encounter is the problem of reloads. Reloads fired in one rifle, then standard base sized, do not necessarily fit into another. They frequently get calls about gas guns jamming, failure to close bolt, failure to extract. The problem is always brass previously fired in some huge chamber. That brass is then standard base sized by the customer, who then finds out he did not size the brass sufficiently to enter the new rifle.
Regardless of die, use a cartridge headspace gage to set up your dies. If you are sizing for a gas gun, size all cartridges to gage minimum.