Axes are used when adjacent to multiple foes, which often indicates high danger and disadvantage.  High Axes skill mitigates.  Confident cleaving increases tactical flexibility, permitting more aggressive and efficient play.  Otherwise avoiding multiple adjacents can be onerous or impossible.  Thus the strongest meleeist weapon training strategy is Axes.

(In reality, cleaving through multiple opponents was an effect not of axes but of great swords, which saw rare battlefield use in that role.  DCSS is not overly concerned with reality.  )

Ideally, train Axes to 1h Broad Axe skill cap of 18, then stop melee weapon training.  Cross-training brings Polearms and Maces near 1h skill caps, making them situationally competitive.

Other melee crosstraining groups are inferior.  They are for meleeists compromised in some way, or tilted to favor a particular weapon type.

Swords were not popular weapons in the ancient world, outside the professional Roman legions, which could close with extreme discipline.  Swords are also inferior weapons in DCSS.  Likewise, a stave is inferior to a spear.

Let this historical tidbit temper your expectations from the Short/Long Blades crosstraining group:  Historically, swords were sidearms.

The ubiquitous popularity of swords in fantasy is due to phallic symbolism and the fact that they look cool and dramatic in combat.  Giving someone a lethal but barely-visible stab with a halberd from several feet away just isn't very exciting for spectators.

The ideal fantasy sword blades are self-lit, colored by team affiliation, move slowly, and make a cool bvvvv sound when moving, with a big kpow when they clash.  This lets even little kids follow the moves of the pro-wrestling dance-fight.

IRL 1v1, sword and shield does beat spear and shield.  However, everyone wears armor.  Therefore, mace and shield beats sword and shield.