Why use bevel instead of mean crease
Simple put, bevel is dope, crease is yuck.
Beveling gives you nice crisp edges, while mean crease is a dirty hack and gives you muddy results. Mean crease is used for when you're in a hurry, or you have objects that are not hero assets and are going to be far away from the camera.
So say yes to bevel and say no to creasing. Unless you have to use crease, like a forced marriage and they are making you marry crease and you learn to love her.
Just like Omar mentioned, beveling edges (either by hand, or by using a modifier) is generally a better option compared to using mean creases, but it is all dependent on what you are trying to accomplish.
The reason mean crease is not super useful in most cases is that it is effectively just "pinching" a 90 degree crease along the designated edge. So while this may have a lot of supporting loops and alter the silhouette, it doesn't shade well since now we have a sharp angle that is supposed to be shaded smooth. For better shading, we need more gradual turns in the shape at a much smaller distance (like a bevel) which is the real end result we are after when increasing poly-count for high-poly models.
When you bevel, we have more control over the profile of the edge, as well as the amount of supporting edge loops to help provide better shading. The shading is important if we intend to see this model up close or use it as the high-poly for a game asset.
I truthfully never use mean crease. Like Omar had insinuated, mean crease is more of a quick hack when you want to sharpen the geometry of a model quickly, however it doesn't tackle the real purpose of what we are trying to do when making a high-poly model, which is to create much higher fidelity shading for our model.