It should be nearly as big as mine. However, nowhere near as big as mine and nearly as big as mine don't mean the same thing. Nowhere near as big as mine means my diamond's a lot bigger than hers. Nearly as big as mine means almost as big as mine.
I'm not sure about not anything like. It's nothing like a cat sounds more natural than It isn't anything like a cat. At least to me. Or perhaps I'm being fussy. Anything like works in the positive. If he's anything like his brother (at all like his brother) he won't cheat you.