Hi Aditya,
By definition the Aspect tool identifies the direction the downhill slope faces. Whereas the Flow Direction tool creates a raster of flow direction from each cell to its downslope neighbor, or neighbors, using D8, Multiple Flow Direction (MFD) or D-Infinity (DINF) methods.
Even though they sounds very similar, they are different. The difference lies in how they are calculated too.
Please review the following two documents on Aspect and Flow Direction.
https://pro.arcgis.com/en/pro-app/tool-reference/spatial-analyst/how-aspect-works.htm
https://pro.arcgis.com/en/pro-app/tool-reference/spatial-analyst/how-flow-direction-works.htm
Put it simply, Aspect uses the elevation of all 8 neighboring cells for computation. Where as Flow Direction (D8) checks the change in elevation in all 8 cell but the result indicates the direction of steepest descent.
Depending on the application (type of analysis you are doing) Flow Direction or the Aspect will be more appropriate.
If you are trying to depict the Surface Flow (the direction what will flow) over a landscape, small or large, I would go with Flow Direction because that is commonly used and well understood. However, if the purpose of application is something different, you have to make the decision based on the application, intended use and the audience.
Hope it helps!
Noman
Esri, Redlands, California