Lightning and co. are turned into L'Cies by a Pulse Fal'Cie that was captured and kept in Cocoon. Lightning and co. are therefore Pulse L'Cies. So far, we've seen Odin, Shiva Sisters, and Sazh's summon (Surtur?). They are all mechanical.
Cocoon is a technological centre. Pulse is a wilderness. But strangely, the Pulse Fal'cie gives Lightning and co. Eidolons which are mechanical in nature. One would think Cocoon Fal'Cies would be the ones to grant thus, but the logic is backwards: Pulse = Mecha, Cocoon = Organic.
Perhaps the Pulse Fal'Cies realized in order to fight Cocoon, you would need the advantage of Mecha over organic, thus they gave Lightning and co. transforming motorcycles, horsey-rides, and racecars and shit?
We've seen those PSICOM dog hound creatures in the demo being "summoned" or digitized out from some sort of digital Esper world. Perhaps those dog hounds are mini-summons themselves? We've seen Carbuncle being handed out from discs, as well as heard of Carbuncle plushies, therefore Carbuncle is "organic" and probably doesn't transform into anything.
Thus this leaves two theories:
1. The Pulse Fal'Cie always give out Mecha summons. Cocoon Fal'Cie will give out organic summons to Cocoon L'Cie (such as our Indian Ozzie Sheila). Reverse logic. Wilderness = Mecha summon, Tech city = organic summon. Like some kind of polar opposites.
2. What kind of summons you get, i.e. Mecha or Organic, depends on what world you're from. Lightning, Snow, Sazh, and Hope are all from Cocoon, which is a technological centre, therefore they get Mechas. Vanille and Indian Ozzie Sheila are (supposedly) from Pulse, therefore perhaps Vanille really does get "Organic" Carbuncle, and Sheila gets the organic Ifrit brothers, Efreet and Affrait?