Just some of my notes:
The upper mids/highs of the G2A are more forward, making them slightly brighter toned, and more in your face (which some people like). However, the downside of this is reduction in balance, causing other elements to fade into the background more. The G1A's are very well balanced, with nothing over-powering anything else, allowing you to hear more of the subtleties, especially in very complex tracks.
The other thing I have noticed is that the G1A's provide more distinction to the sound. For example, two different cymbals sound more different (distinct) on the G1A's than the G2A's, and this carries to everything else. Some of this is the definition of the sound, but also some with the tonal presentation. This becomes even more clear when running the G1A's amp'd. I really like this aspect about G1A's.
When breaking in the G1A's, you definitely need a source with a good amp. After you get 200+ hours on them, the sensitivity is there to allow you to play them quite well off higher quality portable players and computer sound cards. Weaker sources will still need an amp. I can run them off my Sony Walkman (NWZ-S616F) and my higher-end laptop quite well without an amp. I use a NuForce Icon Mobile for my amp, which works well powering the G1A's. It also doubles as a USB sound card, which is great for my crappy work PC and my cheap laptops
If you already at the point of owning, or wanting an amp, I suggest just going for the G1A (and amp). If you just want something to listening to off your portable player, go for the G2A's, as they are an awesome value.