As far as its aspect goes there is not much to say. The differences are so minute that are difficult to see: the White-crested Tyrannulet is cm longer than the Straneck's on average and the Straneck's crown has no or not as much white as the White-crested Tyrannulet. The two useful clues for identification are the season and their voices. So the worst situation is in winter and in silence.
According to Alberto Gurni these species behave differently. The White-crested Tyrannulet is much more restless than the Straneck's Tyrannulet.

PIOJITO TRINADORSerpophaga griseicapilla© Carlos González LedoWinter visitor© Cora Rimoldi

PIOJITO COMÚNSerpophaga subcristata© Claudia y Tito Di MauroAll year round© José Luis Merlo