Here are some photos that illustrate two of the differences between these two species.
L. picta (also L. rossica): "Gena with larger black hairs/small bristles - some of which are at least half the thickness of the bristles below the vibrissa":
L. tesselans: "Gena with only fine hairs (at least some of the lower ones also fair) - distinct from the single line of bristles extending down from the vibrissa":
L. picta (also L. rossica): "Costal cell with a uniform covering of microscopic hairs":
L. tesselans: "Costal cell of the wing with only approximately half its area covered in the microscopic hairs found over most of the wing":
See also this post by Chris Raper at the Tachinid Recording Scheme.