The "active" part of the Nagasaki bomb was an immensely heavy egg-shaped collection of high explosives, uranium metal, a plutonium core, and a lot of complicated electronics. The casing was developed to hold all that together and keep it from rolling violently (which could damage the electronics) and more or less have predictable aerodynamic properties (it was not ideal, but it worked).

If you could see it in an X-ray it would look like this — a very snug fit. (This is taken from a declassified manual regarding the electronics system maintenance of these kinds of bombs.) This visualization gives you an indication of the different parts on display there.

It is entirely functional — there is not really any "aesthetics" or "symbolism" to it, just aerodynamics.

The difference is in the system used to compress the fissile materials in order to create critical mass.

Put simplistically, Fat Man, the Nagasaki Bomb, consisted of a sphere of explosives around plutonium. When the explosion went off, the plutonium would be perfectly compressed. This requirement for an even explosion around the outside of the plutonium hemispheres mandated the spherical shape of the warhead. This large spherical shape thus dictated the shape of Fat Man as, well, a round, fat bomb, with a little elongating to make room for the fuses, circuitry, and a bit of aerodynamic shaping.

On the other hand, Little Boy, Hiroshima's bomb, was a 'gun' type Uranium warhead, in which a slug was fired at a mass. This, reasonably enough, required a long 'barrel' to be fired down, resulting in a bomb which was much longer/thinner in appearance.

So, there is no particular significance of the shape of the bomb, it is simply a case of form following function. The mechanics of the system dictated the shape.