I think the most important aspect is a matter of geometry.
With studded beams, you're constrained by the form factor of the regular LEGO brick, which isn't a cube but a 5:5:6 cuboid. This means that every time you need to change the orientation of things, you'll have to think about how you're going to do it, and use plates and whatnot between beams. It's perfectly possible, but don't be surprised if most of the beams in older Technic models are studs up.
With studless beams, none of that. Orientation of the beams doesn't matter much anymore since they'll fit nicely on a cubic grid. This allows for greater flexibility and, indeed, more realistic models. (Some people also like smooth surfaces better.)
Also, the studded beams had some design issues. The obvious one is the offset between the Technic holes and the studs, which isn't exactly a problem but can still be a nuisance at times. The less obvious one is that the Technic hole in beams is actually slightly too high, meaning it doesn't interact well with the rest of the system. See also this answer and the linked pdf inside for more information on illegal builds. These two design "flaws" didn't matter much when the beams were first created, but nowadays LEGO perceives this sort of incompatibility much more seriously. They still produce studded beams, but I wouldn't venture a guess on how long that will last.
One side effect of the transition is that most studless Technic constructions have odd dimensions, because the studless beams themselves have odd dimensions (presumably, because the number of holes on studded beams were also odd due to the offset). As a consequence, the whole Technic system is undergoing a complete overhaul.
At first, more odd axles have been introduced (most notably 7 and 9), then the universal join was shortened from 4 to 3 (the old one was last seen in 2008, so it's probably gone for good), and more recently the differential has also been remade (there's still one in the 2011 Unimog, but I don't know if they'll actually discontinue it considering it has a function the new one doesn't have.). I don't see any other part left that needs to be updated from even to odd, but considering how often they use a #2 connector just to connect axles, I wouldn't be surprised if they made a 3L version of the axle connector at some point