The Admiral shares pay higher dividends?
No - the admiral shares have a lower expense ratio, but require a higher initial minimum balance ($10k).
There are more than one kind of Admiral shares though. There's the Admiral shares of the total market index, the SP500 index, balanced Index, dividend growth index.... it goes on and on.
My advice is this:
1) convert the shares from American Funds to the Vanguard fund of your choice immediately. Both the SP500 fund and the Total Market Fund are popular here.
2) Once you hit the $10,000 mark, call up Vanguard and have them convert all of those shares into Admiral shares. It won't cost you a thing besides the 10 minute phone call.
3) Later in life if you want less volatilitiy and/or higher dividend payouts (at the expense of some overall growth) you can convert some or all of your shares into an Admiral balanced fund or an Admiral Dividend fund.