The appeal of low-dividend stocks when trading with government debt
In the paper cited at the end of this answer, the incentives for all three parties involved are discussed. Not only did the creditors suffer from a lower return after the conversion, they also faced longer maturities and, given the strong heterogeneity in lending terms across bonds, also a destruction of bond specific information. 

Nevertheless, conversions in line with your description were beneficial for the owners of the converted bonds since the conversion increased liquidity (the liquidity of the shares highly contrasted the illiquidity of government bonds) and reduced the probability of government default. In addition, the shares represented claims on rents of the company. Though, for the specific case of the South Sea Company, there have never been any rents involved. 


  Stephen Quinn, 2008. "Securitization of Sovereign Debt: Corporations as a Sovereign Debt Restructuring Mechanism in Britain, 1694-1750,"
  Working Papers 200701, Texas Christian University, Department of Economics. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=991941