Both bpmn editors should align to the same file extension (.bpmn2 vs .bpmn). .bpmn2 is created by default by web designer and .bpmn by bpmn2 eclipse modeler. This should be solved, so the user who uses processes in both environments does not have to rename them.
Afaik there should be no need to rename (as both environments should support both .bpmn and .bpmn2), but I agree they should probably use the same by default.
BPMN2 Editor now uses .bpmn2 extension as a default. Verified in BPMN2 Editor 1.0.0.201311042148, JBDS 7.0.1.GA (Build id: GA-v20130930-2238-B7).
This BZ has been part of the 6.0.0 stream.