cfan2
1) There could be ways to improve your success rate, but it's hard to tell without seeing your unmatched addresses. Also, when you say 'at the street name level', do you mean you're matching to the StreetAddress locator or to the actual StreetName locator? If it's to the StreetAddress locator, 96% is pretty good, depending on how many addresses you're trying to match. If you need more help with this, you should contact Esri Tech Support.
2) The StreetMap Premium (SMP) product you have is based soley on TomTom (TT) data, which in general is going to be much more accurate than using Tiger data.