Other than one faction being giants and the other dragons what is the difference between the two?
Each faction gives a set of quest armor, and an upgraded set when you reach ally faction. The upgraded (Ornate) sets have clicky buffs that stack with player cast buffs and most potions. Details for each faction are here:
http://wiki.shardsofdalaya.com/index.php/Faction
http://wiki.shardsofdalaya.com/index.php/Scale_Alliance
http://wiki.shardsofdalaya.com/index.php/Stormhammers
I don't see it stated on the faction page, but the maximum faction you can gain from killing enemy factions is indifferent.
The giant BP casts a spell which gives 150 hp and 25 atk, and legs spell gives +25 MR. The dragon BP casts a spell that grants 100 hp and 100 mana, and the legs clicky gives +25 FR/CR.
Going giant faction means that you can farm both greater scales and ornate gems at the same time. Otcho covered the dragon faction pro's pretty well already.
The trash mobs farmed for either faction are fairly even in terms of difficulty imo. Dragon mobs are mostly melee with rampage or weak AE's and are immune to mez, while giants in Stormkeep (where storm giant heads drop) can be clerics that complete heal and stun, wizards that knockback and nuke for 1600(fire) and 650ish(cold) and gflux, Shadowknights that just lifetap for 450 until the end of time. Giants in Storm's Eye (where ornate gems drop) can have a large DS, and cold based nukes that range from 1500-3000 dmg.
For characters geared well above these two factions, giants are typically easier to kill because their spell casting ability becomes their liability when the spells are always resisted.
edit - if you want advice on which faction to side with, Gunder is probably giving you the best advice in telling you to wait to pick one until you have joined a guild. I'd advise killing both though in the meantime rather than steering clear if you can get in on any pick-up raids for either faction. Collect as many giant heads, scales, armor pieces, and drops as you can. Either faction can be raised to indifferent in only a few sessions of farming or raiding the enemy. This way when you do pick a faction some of your work is already done.