Lowther Street would have been a much more affluent area, however only on one side of the road (East Side mostly) where the large town houses are. On the other side of the road were the Old Lanes, which were a much poorer area.
Sue Johnston (actress) did "Who do you think you are" and her grandfather lived in both the Old Lanes and one of the town houses on Lowther Street, I recall she visited the street in the programme. The north end of Lowther Street which led onto Rickergate had more mixed housing, (poor and upper working class) The housing behind the east side of Lowther Street was also very affluent, large town houses.
There was also a school and a theatre on Lowther Street, and quite a few public houses, so not totally up market!
Most of the housing in Botchergate was more basic, small terraced houses behind the main street. It was much more of an industrial area, with factories, railway sidings/sheds etc I think the main part of Botchergate was more of a shopping street, my own family had a shop there, from the 1880's. Behind the main street, again on the east side, there were some more affluent town houses.
Really it depends where your family lived in either of the streets or area. Neither area is either full of poverty or very affluent.