One is a 34S and another is a 38S. DO the sizes often reflect the chest size? (like 34S = 34 inch chest?) Because the 38S has a 42" chest area, and I measured my chest and it's 38" at best (37.5 average).
remember, if your chest measures 38 inches, the jacket measurement has to be bigger than that to fit over your chest. Most of the time, the chest measurement of a jacket is the measurement of the outside of the jacket. So it should be bigger unless you are going for a straitjacket look.
it seems in this case the 38S will fit you. the 34S seems like it will be too tight. it's possible the 36S might fit you, if you like a fitted look.