wideguy

Yes, very much so. There is a very wide range of strength and wear resistance in hardware, as well as corriosion resistance and even temperature ratings.
Everything important to the safe operation of the machine should be replaced with an equivalent, or better fastener.
Head types are sometimes important and sometimes not. As far as the style, designers just like to create new methods of driving bolts and screws so we have to buy even more tools, but, there are also heads (and nuts) that are designed for tension applications, and some for shear. Tension fasteners can replace shear fasteners, but shear cannot replace tension.