There is no specific benefit in TIN according to constitution of the firm whether it is a Partnership firm or Proprietership firm.
However, if you are running a retail business, you can go for the compounding scheme of payment of taxes @ 0.5% on your turnover, provided the turnover does not exceed Rs. 50 Lakhs. In your case, if your turnover is above 50 Lakhs and less than a crore, you still claim the benefit of payment of taxes under compounding scheme by splitting the turnover with 2 firms so that turnover in each of the firms does not exceed Rs. 50 lakhs.
Other than the above, i donot see any other benefit according to the constitution of the firm for VAT purposes.