Both Jazz and Live Jazz are great, but two different birds.
Live Jazz is an effervescent citrus, while Jazz is a subtle oriental-rose-leather scent.
While I think Live Jazz is the better scent, it is the definitition of an informal, fun scent. However, its duration is pretty questionable. If you wear it on bare skin, it will probably evaporate in no time on your skin.
Jazz is a bit more formal, but definitely wearable in a casual setting, and you could wear it year-round due to its lightness. It is similar to Tsar, so if you've ever tried that you should have a very, very, very, very good idea what Jazz is like. It is not exceptionally long lasting, but certainly longer than Live Jazz. I get maybe 4-5 hours out of it, depending on how I wear it.
Personally, I'd get both!