They are similar in every aspect, except color. They are so closely related that can be considered subspecies. Jadina is a poor man, nevertheless legal, Asia Arowana in US. Get a red light to shine at the Jadina, and no one can tell the difference.
Shape (as tlindsey says Asians have taller bodies, Jardini are more torpedo-like), availability (at least for US folks), price and overall beauty -- for which they're really not even comparable imho and very easy to tell the difference between the 2 even if you shine a red light on them) -- as some above said, Jar has 7 scales, Asians have 5 levels (though some call the top scale the 6th scale). Also as Celebrist mentioned there's a higher chance a Jar will be less compatible with tank mates (and seemingly peaceful ones can suddenly snap without notice and you might wake up to find your other prized fish are annihilated).
If you could ever see both side by side in person you can see Asian Arowana have more complex coloration of their scales, which puts them on a whole 'nother level compared to Jars in the beauty and majesty departments.