The study describes the behavior of plasma streamer discharges in helium and argon atmospheric pressure plasma jets fed by dielectric barrier discharge with the specific AC voltage waveform, which has hundred-kHz oscillations deviated from the zero level. The equivalent electrical and gas feeding conditions for producing both helium and argon jets have been provided. The plasma jet in helium is shown to have a diffusive structure and is formed by guided ionization waves, whereas an argon plasma jet is formed by numerous filaments which can have several branches on their ends. Repetitive stepwise plasma bullet formation has been observed in He plasma jet, whereas random and stochastic branching of the streamer has been recorded in Ar plasma jet. Both types of streamers have an approximately equal maximum of their length but significantly differ with the lifetime: they exist for about 1 and almost 8 μs in the argon and helium plasma jets, correspondingly.