It is shabby and the building is run down and filthy in all the places the daily cleaning doesn't get to. It can feel unsafe and even unfit for habitation in hot weather. Extremely hot and also extremely noisy.
I wouldn't say it's cheap based on how low the quality is, but it is very private and Arts District is a nice area... and I guess you get used to the shabby conditions.
Just be prepared for a very bare bones, zero luxury, low comfort stay if you book any of the Sogo rooms.