Whether rye was similar in taste to Irish whisky was asked earlier; certainly both are quite different from Scotch but that only makes them similar in the sense that all red wine is the same

Ignoring the mass-market products (which are trying to be bland), Jameson is generally sweeter, lighter and more watery than rye, while rye has a unique flavour (not like rye bread, but on that line) and more viscous. Fine rye is remarkably nuanced and under-rated, making it cheap (at least in the US which doesn't tax alcohol much).