Actually Dwarves get a gun bonus, not an axe bonus. And i dont think paladins can use guns.
Humans get the increased spirit bonus, helping you regain mana/hp during downtime (And mana during battle if you arnt chain casting). Dwarves get the treasure finding ability that helps them locate treasure chests, so I guess you can make extra money that way.
Humans have quite abit more agility (better armor) and slightly higher int (for more mana), and better spirit than a dwarf. Dwarf gets a bit higher strength, and significantly more stamina (hp).
Dwarves will deal more damage, and can take more damage and get the racial ability to become immune to poison, disease, and bleed effects, along with natural frost resistance.
Humans can mitigate damage better (take less per hit) but have less hp (DoT effects will affect them more significantly), a little bit more mana for casting with, and lower downtime due to the higher spirit (also better mana regen rates during battle, additional spell casting). They also get a bonus for using swords, and are better at detecting invisible units (really useful in pvp)