It depends on what you mean by obvious. If you compare 8x10 prints from 35mm XP2 and 35mm Delta 400 side-by-side, both exposed the same subject under the same lighting condition, the difference is obvious.(posted 8150 days ago)C-41 based (chromogenic) films have lower resolution, finer-grained appearance and softer highlight contrast. Besides, your control over images through film development is much limited with chromogenic films. If you have at least an intention or desire to control images through this process, I recommend regular b&w films.
I can think of one application where chromogenic film may be preferred in terms of image quality -- portrait (especially of female models). Not that this would be my preferred choice.
Just because it has finer grained appearance, there is a temptation for some people to assert chromogenic film is sharper - incorrect.