Most of the time dwarfs are rather "bud-kicking for goodness" while gnomes are more the trickster kind.
It does really depend on what sort of character you want to play. The stereotypical member of each race is very different.
Gnomes are more inherently magical, whimsical and charismatic. They are also small-sized, which is a bit of a bit of a drawback for a fighter-type character. With their Charisma bonus they can make very good Bards, Sorcerers or Oracles.
Dwarves tend to be stoic types, tough and practical. They have an affinity for the Earth and value craftsmanship and community. Their gods tend toward the Lawful and Good end of the spectrum. Despite being short, they are stocky and still count as medium characters. With their high Constitution and Wisdom they make solid fighters and clerics, though I suppose they could also do well as Empyreal Sorcerers.
This is a complete generalisation though. You can play any class with just about any race and do well. Pick something you'll enjoy playing.
Choosing either also really depends on whether you're going Golarion or homebrew. Look into the fluff either way to help determine if it fits the character you want to play or if it inspires you to play a particular character.
Corvino has the right of it otherwise. The only thing I'd add is to further emphasis class choice. You can play a non-empyreal sorcerer dwarf but you'll be penalized right off the bat just like a gnome fighter would be. It should be a factor but not the only one.
Stereotypically they couldn't be more different.
A gnome is like a 5 year old child.
A dwarf is like a grumpy old man.
