I don't own both but I used to...
Now I just have 55. I do miss the rendering qualities of 43 but I'm much more comfortable with focal length of 55. If you have and love 77 then 43 would make a good sense, that is however if you are comfortable with the focal length. But it's a nice spread 43+77, 55 is touch close to 77.
Now to the 2 lenses...
43 is much smaller, uses smaller (49mm as on FA77) filters is lighter and focuses faster (not fast, but faster than 55).
On the other side, 55 is quiet, is WR and has better hood and hood attachment arrangement (the DA*55 hood offers much more protection to the front element from elements, hits and debris than any FA ltd hood).
IQ wise? FA43 is incredibly sharp at any f stop, has excellent contrast and great colours. DA*55 is usably sharp at f1.4 just about as sharp at f1.8-2 as 43ltd and sharp from there onwards (43 edges it in this respect though). Contrast is very high from f1.6 and usable at f1.4. 55 has less CAs than 43 and I'd say touch less PF too. 43 has bit better flare resistance IMO and touch better colours. OOF? well, both lenses can be busy. 55 more so in "right conditions" but also because of extra 12mm 55 smooths background more in most occasions.
At the end few shots from both, you tell me which is which
regards