At the risk of over-generalizing, here's the difference: Gore-Tex remains the most breathable waterproof out there, particularly in its newest XCR iteration. However, the "Gore-Tex wannabes" all offer good to excellent waterproofing, adequate breathability, and generally much lower prices. Mountain Hardwear's Conduit-based Exposure II Parka, for instance, sells for $260about $140 less than Mountain Hardwear's Gore-Tex-based garments of similar design. And some of these pieces are really incredible bargains. Marmot's Precip Jacket, for instance, has been a raging success in the outdoor world, with features that include a clamminess-fighting lining, full hood, and pit zipsall for the absurdly low price of $99. And it's a good jacket. I'd take it anywhere for general-purpose backpacking. Maybe not for a month in the rainforest or up Mount Rainier, but anything else, sure. I've also had very good luck with Lowe Alpine's stuff and Patagonia's non-Gore-Tex offerings, such as the $199 Torrentshell Jacket.
Anyway, my point is that among the non-Gore-Tex jackets there is not a ton of difference. (The makers protest to the contrary.) Get one with good features, that looks well-made, fits well, and has the right price tag attached.