The question of whether it's worth it or not is tough to answer, as that's kind of an individual decision. For me, I figured this might be the only time I'd have the opportunity to dive the Adriatic, and I wanted that new experience. I also had 3 full days in Dubrovnik, so I didn't feel like I was giving up much sightseeing time to do it.
From a cost perspective, I believe it was 100 Euros per person for the 2 tank boat dive, including equipment and pick up at the hotel (we took the bus back).
The coolest part of the dive for me was the different terrain. Our first dive was down to a max of 100 feet, and we explored three caverns at different depths. The second dive was shallower, and we did a swim-through cavern and saw the remains of a wreck. Marine life was fairly limited compared to the diving I've done in HI, CA, and the Caribbean: 2 moreys, a big school of bait fish, a few nudis, and a small amount of coral.
I'd say that if you have a couple days in Dubrovnik, and are excited about diving different places in the world, it's worth it. If you're a more casual diver and don't have much time in the city, you could probably skip it.
Also, while in Dubrovnik I recommend the tram up to the fortress up on the hill. The fortress isn't anything special, and it's not especially cheap, but the views and pictures you'll get are worth it.
James