Let me start by saying (if you weren't aware) that I am the author of Naval Thunder. GQIII is a good system, so I'm not going to run it down, but let me tell you why you want to go with Naval Thunder:
Complexity
As Dave mentioned, its simpler to pick up. The basic game is written to make it easy for people brand new to naval wargaming to get started. I teach the game at conventions all the time, and pretty I much don't have to do anything past turn 3, they run it themselves.
Gaming "Richness"
As much as I respect Dave's opinion on things naval, I don't know if I would agree with Dave on the richness of the gaming experience.
The Naval Thunder rules come with dozens of modular, optional rules you can pick and choose from to add to the game. Depending on what you think are the fun or most important parts of naval warfare to model, the rules are there for you to use, or not use at your discretion. You make Naval Thunder into the game you want it to be. Stick with the basics, dive into the detail, or just add little features here and there as you go along – its completely up to you.
Charts & Tables
Naval Thunder is *definitely* not chart heavy. Every chart in the game fits comfortably on 1 side of 1 sheet of paper. By your second game you will probably have most of them memorized anyway.
Personally I hate cross referencing charts and tables all the time. Naval Thunder is designed around "immediate gratification" when you roll the dice. You know what you need to roll and know the outcome as soon as the dice are rolled. Much more exciting than having to cross reference results against tables IMO.
Dice
Not sure what you mean by "dice heavy." I don't think most players find it so. Ten dice is about the most you would ever roll at one time. Shooting process is roll to hit, re-roll dice that hit looking for armor penetration, roll criticals if any. At each step of course there are fewer dice to roll than the step before. Figuring out what you need on a roll takes only seconds. By the mid-point of your first game you will be able to resolve the attacks for every single gun on a battleship in under a minute.
Aircraft & Subs
Airplane and sub integration is seamless and fast. Naval Thunder focuses on modeling realistic affects of air/sub combat on the surface action – rather than adding a lot of complexity or "mini-games" to the rules. I'm not a big fan of carriers or subs. . . but I have to admit – both are a lot of fun in Naval Thunder.
Big and Small Battles
Depending on the level of detail you choose to add, Naval Thunder can handle anything from thrilling single ship duels, to huge fleet actions. At GenCon this summer I ran Jutland to completion in 5 1/2 hours – including teaching the game to most of the players. 72 battleships, battlecruisers, (and a few armored cruisers) on the table.
I don't know of any other systems that can make that claim – except maybe some that are so abstract you could be playing anything – no naval flavor at all.
The secret is that movement is simultaneous and an entire side can be resolving its shooting all at the same time. In the IT world we call it "simultaneous multi-threading." Basically it means people are actively playing the game almost all the time, instead of having to wait around for others to finish their turns.
Anyway, hope that helps some. You can learn more about Naval Thunder here:
navalthunder.com
Or pick it up here:
link