Accuracy does not depend on the type of satellite images use in the classification. Instead if will depend on the algorithms or methods of classification. For example, the ML-based classification will give better results as compared to general classification methods.
For delineating the urban built-up area there are different satellite-based index like NDBI, EBBI, BU, UI, IBI, VrNIR-BI. You can try this index, which would evaluate better for your area.
It is related to your project accuracy that you want. For example, Landsat images are suitable for vegetation cover classification. All of images have different results for different works.
Depending on the scale of your work and available budget. I have used RapidEye (resolution: 5-20 m) with good results (https://earth.esa.int/eogateway/catalog/rapideye-full-archive-and-tasking?category=Data)
Apart from distilling what is common to all land-use/land-cover classes, producing robust result in your task is dependent upon the classification method and resolution of the images used.
Types of satellite images used in classification have no corellation with the accuracy but is depended on the methods used in classification. For example, use BU, IBI or VrNIR-BI satellite based index for delineating the urban built-up areas
Better the resolution better will be accuracy, also number of bands will improve results (In case of Satellite based Built-Up Index). Accuracy also depends on the number of training sites and classification algorithm.