From the PHP Manual:
mysql_fetch_object() is similar to mysql_fetch_array(), with one difference - an object is returned, instead of an array. Indirectly, that means that you can only access the data by the field names, and not by their offsets (numbers are illegal property names).
Speed-wise, the function is identical to mysql_fetch_array(), and almost as quick as mysql_fetch_row() (the difference is insignificant).
I generally don't have use for an object when I query a DB, so I use the mysql_fetch_array() functino personally. I find arrays to be a bit more flexible and easier to manipulate.