Sorry "Breeze" not Bliss. (first message of the day).
About the weather, if it is a hurricane they will change itineraries, but not if it is just rainfall or wind. It has to truly endanger the ship before they will change routes.
There is not much difference between the East & West, and if you ever do a second cruise you can go to the other one. I generally like the West because of snorkeling with the stingrays in Grand Cayman, some of the beaches in Cozumel, etc. But you can also find great beaches in the East. caribbean, too.
So, to give you a real answer I looked up the two routes, and I think I might prefer the East. Just be aware the islands are more populated, shopping is a main attraction. Nassau has Atlantis (cool for day), San Juan fun for just walking around, St Thomas has nice beaches for snorkeling and shopping, Grand Turk is something of a tourist trap.
East: Nassau, The Bahamas
San Juan, Puerto Rico
St. Thomas, USVI
West: Cozumel has nice beaches. You can do a "resort scuba dive with no license". Costa Maya has some Mayan ruins. I have not been to Belize or Roatan, but I think a lot of people would say they are not that interesting.
west: Ports of Call: Cozumel, Mexico
Belize; Mahogany Bay, Isla Roatan
Costa Maya, Mexico
Being October I would guess you stand a chance of better weather in the West, although its always a crapshoot.
But really, just pick one and go. I would be more concerned about the ship than the itinerary. As for funship 2.0 the biggest difference is food & entertainment. 2.0 gives Guys Burgers, Redfrog Pub, Alchemy Bar, Comedy brunch.
Dream still has good entertainent & food, though. I think you might even prefer some of the shows.
But it's your first cruise, right? You will have a great time regardless of which one you pick.