I always play as the Eden Initiative. Am I missing out on anything by not playing Global Trust?
The Global Trust tends to use much more efficient buildings for resource acquisition and powering structures, but at a cost of having a detrimental effect to the environment.
The most obvious one players will notice is the ability to mine iron and coal far more efficiently than the Eden Initiative. Their buildings tend to take up more space however, and generate a significantly worse impact on the ecosystem.
As your cities level up, you'll find that not only can Global Trust generate much more in resources, they also tend to generate a lot more funds than the Eden Initiative (they have Casinos).
You should decide carefully which pros and cons you feel better suited to playing with when deciding which faction to choose.
Eco-friendly, but weak in resources? Or industrious, but polluting?
Either way you play it, both sides have their pros and cons to balance each other out. They can be equally as difficult to work with.
The short answer is 'not really'. The fundamental mechanics are the same, and I'd say the complexity of each faction's supply chain is about equal. Playing either faction feels about the same, aside from a few small differences which IMO the game doesn't really do enough to emphasize... aside from making Tycoon islands look very brown.
A number of Tycoon and Eco techs compliment each other, so you're limiting yourself if you avoid Tycoons altogether (particularly on continuous+large games). Tycoon resource extraction tends to be more compact, so you can squeeze more out of your land early on, but at the cost of more eco damage. Tycoons also generate more cash, but this is offset by the fact that eco farms can be made a lot more productive because the Eco tech can push an island's eco score very high, allowing farms to overproduce.
Playing a different faction probably won't rekindle your interest in the game if its fading, but I'd definitely recommended mixing it up if you're still looking forward to spending a lot of time with it.