Which internship would be better experience?

So, I have a question about which type of internship would be better for me.

First off, my background is in Math/Stats. Bachelors in Math, getting a Master's in Statistics, graduating next year. No background in finance though. I've been doing a lot of research on quants and am very interested in getting into that full time when I graduate.

I have an offer now for an internship with a data mining firm. Does a lot of work for the government. A big positive for this is that I would get a ton of experience in data analysis and this might look really good for quant positions. A negative is that I still wouldn't have any experience in finance.

I've sent my resume to a lot of small financial firms without much luck. My second option would be approaching these firms again and asking to intern as an analyst for free. Might get something. A positive is that I would get something on my resume in the financial industry but the level of analysis I'd be doing probably wouldn't be anything too fancy. Probably not as intense as the other internship.

Which do you guys think would be better for me to get into banking/quant full time next summer?

Thanks