Yes, there are quite a few advantages.
Most important: Math italics are available at several optical sizes -- extremely nice for typesetting material in TeX's script- and scriptscript-sizes.
Beautifully styled, "real" curly braces at all sizes. With
txfonts, as with the regular
LM fonts, most of the tall curly braces are really straight with only the very top and bottom parts being "curly";
Beautifully styled radicals (square roots);
Good-looking sum and integral symbols;
Upright and slanted uppercase Greek letters;
Easy to typeset entire formulas in bold (as opposed to only the letters);
Better positioning of subscripts; and ...
If you get the "full" version of the package (the "lite" version is free of charge, by the way), you also get specially styled fraktur, script, and blackboard-bold math alphabets.
A longer and more-detailed listing may be found in the User Guide of the MathTime Pro package.
Do note, though, that
mtpro2 provides only math fonts and no text fonts. Thus, if you do use and load the
mtpro2 package, you'll still need to issue a command such as
in the preamble in order to get Times-style text fonts.