Probably that.
A purer (fewer high overtones I guess - less "oboey" if you like) sound generally. Minimises the differences in octaves - a smoother tonal transition from C2 to D2.
More stable intonation. A hard reed on a close mouthpiece is a lot easier to play in tune with than a soft reed on a wide mouthpiece.
I can't say that they're particularly easier to play for long periods - but that maybe more to do with the style of music than the mouthpiece/reed.
I'm inclined to think that achieving a "classical" sound is only worth pursuing if either, a) you really like that sort of sound, b) you need that sound in order to join a conservatoire/orchestra/chamber group, or c) you like a challenge. If it's just you then you can sound however you like.
@David Roach has done a considerable amount of work on this sort of thing - perhaps he'll chip in.
From my POV, on reed instruments generally, the better one can keep the integrity of one's embouchure from top to bottom, the better the extremes of an instrument will work. On a modern sax it is highly desirable to keep the embouchure as still as possible and (theoretically) control intonation by manipulation of the vocal tract alone. Obviously sub-tone necessitates moving the lower jaw back, and sometimes a shift forwards can help extreme high notes, so, to quote that timeless epic 'Pirates of the Caribbean' it's 'more of a guideline'.
Joking apart however, since one tends to use a stiffer reed on a closer tipped mouthpiece - and classical mouthpieces are usually close tipped - one could say that it's easier to achieve good top tones on a classical mouthpiece.
Every mouthpiece, presuming that it's well faced, will generally work best with a certain stiffness of reed and it's really up to the player to build embouchure strength through practice to get to the point where their reed is stiff enough to support the entire range of the instrument with the minimum of embouchure movement. This does not mean that the reed has to be mega-hard, don't rush out and by boxes of #4s! But it does have to have enough resilience to support the top tones whilst allowing the low ones to sound.
My own experience has led me to these guidelines (!). If one were to use a Selmer C* or C** or Vandoren S15 or SL4 (my go-to classical choices), one could get good results by using anything between a 2.5 and 3.5 Vandoren Blue Box reed. Bear in mind that a 2.5 will tend towards a rather light and thin sound and a 3.5 will need a developed strength. I generally use strength 3s on these mouthpieces unless I've been hammering away at Nyman for a couple of weeks in which case I will need the 3.5s (or even a 4 on occasions, but I'm not as young as I was!).
On a Vandoren S6 or 7 or a Pillinger 150/160 I will generally use a Java 3 or a V16 3 or similar (Lupifaro 3 or 3.5; so something commensurately softer for a more open mouthpiece because these reeds come out a half strength softer than Blue Box.
The point I am making is that although the student may need to use a #2 or even less stiff reed, one is unlikely achieve a full range with good tone and intonation until one can comfortably step up to a stiffer reed. And I do mean COMFORTABLY step up; it's no good whacking on a too hard reed when your musculature is not developed to use it!!
Whether it actually comes out sounding classical or otherwise is not much to do with this, because the sound one makes is governed by the sound in one's head. I know a very fine Jazz player who uses almost the identical soprano set-up to my classical one and sounds entirely different to me.
