Maybe. A retrofocus lens must have barrel distortion (and a telephoto lens must have pincushion distortion). Correction cannot be complete in an asymmetrical lens, and prime lenses in the 20mm (35mm equivalent) range typically have around 2% barrel distortion (Zeiss 12/2.8 2%, Zeiss 21/2.8 1.7%, Sigma 20/1.4 2.4%, Canon 20/2.8 1.9%, Nikon 20/1.8 1.6%, Nikon 20/2.8 2.3%, Pentax 21/3.2 2%). According to Photozone the Fuji 14/2.8 has 0.4% measured distortion and the 23/1.4 less than 0.3%, in both cases the same in RAW and JPEG. Those are incredibly (literally) low values. There has to be a suspicion that they are correcting the distortion in RAW.
The 14/2.8 has 2.4 stops of light fall-off at f/2.8 and 1.8 stops at f/4. There are no direct comparisons but the Nikon 20/1.8, eg, has, on FX, 1.2 stops of light fall-off at f/2.8 and the Nikon 12-24/4 has 1 stop of light fall-off at 12mm and f/4. The Fuji 23/1.4 has just over 2 stops of light fall-off at f/1.4. The Nikon 24/1.4 has 0.9 stops of light fall-off on DX at f/1.4.
Of course, everyone decides for themselves what is acceptable, but it is clear that the mirrorless user pays a penalty.
Let's compare these figures to two Nikon mount 20/21mm lenses. The Nikon AF Nikkor 20/2.8 has a vignetting of 2.26 EV at f/2.8 and the Zeiss ZF.2 21/2.8 has a vignetting of 1.99 EV at f/2.8 which is less than 0.5 EV difference from the Fuji 14/2.8 at f/2.8. It is well known that all lenses will vignette less as you stop them down, so comparing a lens that starts at f/1.8 to one that starts at f/2.8 may be a skewed comparison.
Let's consider distortion, and compare the Zeiss Loxia 21/2.8 for mirrorless Sony and the Zeiss Milvus/ZF.2/ZE 21/2.8 for DSLRs. Both are retrofocus Distagons.
Zeiss Loxia 21/2.8:
http://www.zeiss.de/content/dam/Photography/new/pdf/en/downloadcenter/datasheets_loxia/loxia_2821.pdfZeiss Milvus/ZF.2/ZE 21/2.8:
http://www.zeiss.de/content/dam/Photography/new/pdf/en/downloadcenter/datasheets_milvus/milvus2821.pdfFrom the graphs for distortion, we see both lenses have very similar, about 2% barrel distortion without any digital correction applied.
The graph for vignetting indicates approx. -2 EV for the Milvus/ZE/ZF.2 (DSLR) lens. The graph for the Loxia (mirrorless) indicates less, but I think that one is digitally corrected.
Both the mirrorless and the DSLR Zeiss 21/2.8 show very similar quality MTF graphs, though the mirrorless lens has a more gentle curve drop off toward the corners, where the DSLR lens drops more abruptly near the edge.
The takeaway for Zeiss is that distortion is comparable for the DSLR and mirrorless lenses.For the Fuji 14/2.8 and corresponding full frame DSLR Nikon 20/2.8 and DSLR Zeiss 21/2.8 the vignetting is actually comparable rangin from 1.99 EV to 2.4 EV. My guess for the Zeiss Loxia 21/2.8 is an uncorrected vignetting between 2-2.5 EV.
In summary it appears that little, if anything is given up with mirrorless wide angles. In the case of Zeiss, the mirrorless Loxia 21/2.8 weighs 398 grams, about half of it's DSLR sibling, so some weight is lost.