I love my nexus 7 as it fills my android appetite just enough so I don't have to worry about my phone crapping out because I bricked it with a rom. But I will be selling the iPad 3 for 2 minis for the kids.
If the mini comes anywhere close to the rumored $299, it's because of competition. People will pay an 'Apple tax' to a a point. But if this comes in priced double the competition, sales will suffer.
Of course the iPad Mini will beat the Google Nexus 7 sales-wise. Apple relies on uneducated and ill-informed consumers, of which they have plenty.
You should check your math. Doubling $199=/=$299.
OP, this is a very poor thread. You don't set the parameters that the mini must meet to "beat" the nexus 7. If you were asking about price, it's likely the nexus would win. Unfortunately, we're not 100% positive about that either, because we know nothing besides seeing a few pictures that purport to be the mini.
We can't make educated guesses without some information; doing so makes us no better than those whackjobs who believe in creationism/intelligent design.
How about we wait until after the announcement before speculating on whether the mini can "beat" the nexus 7?