The only differences so far are the seeds you start with (though all races seem to start with wheat), race specific armor/weapon/food recipes you start with, and like you said, cosmetics including your spaceship and randomized names during character creation.
Chucklefish didn't want one race to be able to do something that another couldn't. All race specific recipes can be found by other races later in the game so everyone will eventually have access to all the same things.
The maybe not-so-noticeable cosmetic changes would be what one race has to say about another races technology, using the magnifying class on the right of the screen. For example, my Hylotl commented on the torture devices and large green cloning(?) tanks in the Apex outposts very negatively saying such things do not belong in civilized societies.
Your race will not affect how other races act towards you. If you stumble across any villages, they will pay you no mind (as long as you don't have a weapon equipped) and merchants will sell to you. If you come across a dungeon, you will be attacked on sight. Even if you are the same race as the dungeon.
Update for Upbeat Giraffe released 1-29-15:
A new class has been added, the nova kid! The most interesting part about this class is their starting weapons include ranged weapons unlike the other classes that only get melee weapons.
Other than the nova kids, anything class-specific still seems to be cosmetics (starting armor, craftable weapons, recipes, etc.), most notably added in this update your ship's AI (S.A.I.L.). Also added in this update was the ability to upgrade your starting ship. These upgrades add sections to your ship giving you much more space to decorate, set-up a farm, or really anything you would want to do on your own gigantic spacecraft. Each classes ship has it's own unique style.
Planets in different/later sectors can have different allocations of ore, as well as different Biomes not available in the Alpha sector.
Note that the ore distribution differences can be a double edged sword - if you are doing something that needs Iron (say, you downloaded a new mod that requires Iron for its crafting station) but your home planet is in Delta or X Sector, you're quite unlikely to find it in any reasonable quantities. You'll also be unable to build your planet on a Tentacle or Magma planet in Alpha sector, because they aren't present there.
The flipside to this, however, is that on lower-level planets (like in Alpha sector), you're at considerably less risk of murder, mutilation, and mayhem caused by the local wildlife. Even Impervium armor only goes so far on threat level 10 planets in Sector X, but it will basically invalidate the threat of enemies in Alpha Sector.
Best Answer
Pickaxes are now used as a short-term method to mining slightly faster than the Matter Manipulator. They can no longer be repaired but are now much cheaper to craft. They also have a much more limited range than the Matter Maniplator
It seems 2 handed weapons of higher rarity, that shoot projectiles can damage nearby blocks (the projectiles won't damage farther away blocks, only the swing from the weapon itself). They can hit many more blocks than a pickaxe will, but take more hits to mine. You will also not be able to collect any blocks destroyed in this manner, so highly non-recommended.
You can use both the projectile or weapon's swing to destroy background objects like plants and the destructible white chests, these you will be able to collect. This doesn't work on farm-able plants, just things like reeds in desert oasis' or jungle plants.
They can be crafted at an Iron anvil, or found in containers in some dungeons.