What would be the problem with this?

Aralvar

See how one of them is made more professionally by having the block extruded from the shape, and the other is simply a block that has had the bottom dragged through the shape? They look the same, and the latter decreases poly count and is easier. So what exactly is the problem with this? Is it something that doesn't really matter but people do it to seem more professional, or does it actually matter?

I ask this because I'm doing something like this on a larger scale where extruding the shape from the object could add an additional few hundred polygons to the polycount (which is already fairly high on the object I'm making).

Bek

This is commonly called floating geometry. Depending on what you're doing it might be a good idea, in other cases it might not. This thread has a good example and explanation of the pros and cons: http://www.polycount.com/forum/showthread.php?t=117017

The wiki might have more info. You should consider vert splits (http://tech-artists.org/wiki/Beveling) to see which one is 'cheaper', and if you're normal mapping that changes things too (see http://www.polycount.com/forum/showthread.php?t=107196).

In your example also, the box extends unecessarily into the cube, which will be a waste of UV space.

cryrid

The one on the left could also have it's triangle count reduced further.