Both. They could lack in the appearance department, but personality is more favorable and vice versa.
I did the net of fury too! When he pinged me to move out, I told him he should, but then he changed his mind. So I kept using the net until I found out about the TT trick.
That's what I feel about Beau, sigh...Appearance matters somewhat but if their house is hideous even if they are cute, i can;t accept them lol.