The Dawnflower Dervish archetype specifically says "All other types of bardic performance work normally (affecting the bard and his allies, or the bard’s enemies, as appropriate)."
The Dervish Dancer archetype has different wording, but it never says that it replaces the bardic performance ability, so I'm going to assume that it's intended to work the same way.
Note: I'm also assuming that D20PFSRD has the correct wording for both archetypes.
The Dawnflower Dervish will get every Bardic Performance except Dirge of Doom assuming you stay in the class long enough.
The Dervish Dancer gets Countersong, Distraction and Fascinate but loses Suggestion,Dirge of Doom,Soothing Performance,Frightening Tune, Mass Suggestion and Deadly Performance assuming you stay in the class long enough.