Private schools are expensive because they're private, not because they're any better than public. If you'll still have the option of going to the private school next year, I would wait. Then you can pick which one you want.
I went to a public school for undergrad and a private school for law, and so far I have only observed two differences: (1) sometimes at my law school there are cookies and/or free drinks, (2) my law school costs about $33,000 more per year than my undergrad did - and that would buy truckloads of cookies and beer.
50/50 is low odds these days because it's getting more competitive every year (assuming you're using last year's numbers as a guide, keep in mind that next year's numbers will really be two years later), but while you can't control the function, you can certainly control the input. Why not retake the lsat for a couple more points and strengthen your application with a really good personal statement?
Plus - you can save up a little money while you wait. A penny saved is probably about three pennies earned in your situation: Loans will about double the cost of law school, and taxes (if you make lots of money as a lawyer) will take another big chunck.
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