I'm not sure of technical details and I'm not really interested in the engineering aspect, but...
That Avalon is gonna have internal components and an engineering team that are probably worth the 10 times (in price) you see. Additionally, the EQ is gonna be more accurate and won't crap out as quickly when you load it on. IE a -10db cut @ 400Hz is gonna sound more natural on the Avalon than on the Rane, even if it imparts a different sound.
IMO the Avalon would just sound a lot better than the Rane.
I'm not gonna bash the Rane as I'm looking at a couple up for auction right now, but if I had your budget, I would buy both and return the one that has the higher suckage factor.
I do wonder though...why would you run your mixes through an EQ? Unless you're mastering, that is.