http://www.roland.com/support/article/?q=manuals&p=INTEGRA%2D7&id=62482120
http://www.roland.com/support/article/?q=manuals&p=JUPITER%2D50&id=62467123

These are the sound lists of Integra and Jupiter.
You'll see that the Integra has all the supernatural acoustic sounds the Jupiter has, but more.
In the supernatural synth section, the Jupiter has a few additional, but rather average, acoustic tones (e.g. trumpet sections) which you don't find stored as a tone in the Integra, but still as a waveform so you could edit and store these few tones yourself - but it's pointless because the Integra has much, much better versions of those sounds in the SRX expansion section.
The integra does not sound thinner, there is absolutely no difference to the identical Jupiter sounds. I know some Jupiter owners who are angry they bought the Jupiter before the Integra came out. It must be due to the varying audio quality of Youtube demos if you think there is a difference.
Have you listened to these official demos?
https://soundcloud.com/rolandcom/sets/201208-snat
https://soundcloud.com/rolandcom/sets/srx-10-big-brass-ensemble
https://soundcloud.com/rolandcom/sets/srx-04-symphonique-strings