I learnt from here that there is no major difference except that the <bgsound> tag should be included in the <background> tag.
The output will vary in each case though. The <bgsound> tag will cause the file to be played in the background whereas the <embed> tag will make the midi file appear as an object on the page- thereby enabling the user to turn on/turn off the music as he wishes.
More info here.
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