I would do the same stuff: Study tactics, endgames and middlegame strategy, and I wouldn't bother about the opening.
I'd also like to mention that your hypothesis makes no sense. According to the rules of the game, one can play ANY legal move he fooking pleases.
...reminds me of a bookshop I once visited.
The ruy lopez 
I'd play the Najdorf every day of the week, and twice on Sunday. First, most dragon games are met with the Yugoslav Attack. You can just depend on that being white's answer most of the time. The rest of the time, white doesn't have any preparation memorized or available. The end result is that the dragon, despite its fearsome reputation, is somewhat predictable.
The Najdorf, on the other hand, has a number of equally valid lines for both white and black. I used to be a Dragon adherent but switched to the Najdorf. I have seen several move 6 responses that all lead to interesting theory and there isn't a single line that is clear-cut better than the others, as opposed to the Dragon. It just winds up being a more varied and interesting variation at the end of the day.
Najdorf -> You can go into Opocensky! ;)
I would do the same stuff: Study tactics, endgames and middlegame strategy, and I wouldn't bother about the opening.
I'd also like to mention that your hypothesis makes no sense. According to the rules of the game, one can play ANY legal move he fooking pleases.
I am finding this out after many years of playing. I accidentally discovered it earlier in my chess playing days when I wound up with a tactics training program. I played it constantly, and my rating went up considerably - I assumed it was because I was burned out and just started doing problems, and the rest was really what I needed. That has not been the case.
In order to improve my own chess, right now I am committed to a) doing at least 50 tactical problems from the tactics training program on chess.net and b) I am not playing blitz games. Tons of blitz over the years has made me undisciplined. I want to move right now, before I have developed a solid understanding of the position. That is a mistake in longer games, but I have had standard games at a 30 min time limit where I lose and only used 5 min on my clock. I'm not doing that any more if I can help it!
Najdorf -> You can go into Opocensky! ;)
Actually White chooses the Opocensky, not black.
Edit: Oh I see some people call it another Opocensky variation if black plays e5. That is ridiculously confusing to have two openings of the same name within the same subvariation of the Sicilian, personally I would rather the more established naming convention of 6. Be2 regarded as the Opocensky variation and the 6. ...e5 called the classical or something.
True. Opocensky tend to be 6.Be2. Modern line is after Be6 or Be3, I don't know... 6...e5 should be "main line".
I would play the Dragon it is easier to play. The Najdorf relies on long forced variations where natural moves are often wrong. Leave the Najdrof to the professionals. You can play a decent dragon just knowing some of the themes.
Add another vote to the Najdorf column. My reasoning is similar to Beachdude's and msc157's, to which I will add that I love playing the Yugoslav as white, and if black, it would scare me.
First of all, playing different openings is good for your chess, especially a player seeking to improve (you don't really need deep specialization until you play GMs). Ideas from many openings are transferable to others, especially within different sicilians. For example, the idea of a timely ...Rxc3 is a good move to look out for in both the Najdorf and Dragon, as well as a white knight arriving on d5.
When it comes to "theory", the dragon is really much more theoretical than the Najdorf. The value of every move is extremely high, even more so than the Najdorf, because both sides usually attack each other in such direct fashion. The dragon, as "fearsome" as it is among amateur players, is actually the safe choice for the super GM, as with best play it typically leads to advantageous, although only marginally, endgames for white, which black can usually hold. The online database of chesstempo confirms my stipulations; in games betwen two 2700+ players, %60 of dragon games are drawn, compared to just %46 of Najdorf games, and black only wins %17.8 with the dragon, while that rises to %22.3 with the Najdorf.
Both variations are complex obviously, but the Najdorf definitely is more complex, although less theoretical, precisely because of the flexible nature of the position. In the dragon, long calculated variations and knowledge of theory is more important than feel for the position than in the Najdorf, but because of its forced nature the dragon would probably be "easier" to play than the Najdorf. For example, if you played a GM, you would have to play the Najdorf with a much deeper knowledge of chess than you would the dragon, because of black's narrower choice in the dragon. I'm sure this is a much longer response than you wanted, but if you take the time to read it I hope you can garner something from it.
Why not Scheveningen, or Classical, Taimanov, Pelikan, Kalakashinov???
People always forget these classics!
I like Dragon, because if your opponent doesn't know what they are doing, (meaning they don;t know theory), a Rxc3, Nxg4, Bxc3, Qa3+, and Qb2# will crush them!
The dragon, as "fearsome" as it is among amateur players, is actually the safe choice for the super GM, as with best play it typically leads to advantageous, although only marginally, endgames for white, which black can usually hold. in games betwen two 2700+ players, %60 of dragon games are drawn, compared to just %46 of Najdorf games, and black only wins %17.8 with the dragon, while that rises to %22.3 with the Najdorf.
Thats funny, because I heard somewhere (probably from Fischer) that 9/10 games in the Dragon are won by White, not drawn.
Fischer lived about 100 years ago though, his thinking is well out of date.
"if you were forced to play Sicilian hypothetically every time, would you play the Najdorf or the Dragon more frequently and why"
I have to give credit to your captors here for mental confusion factor. You have to pick one to play every time, yet you can play one more frequently than the other, which sort of implies that you can still play both...
Anyway, we need more information regarding your captivity:
1. How are they forcing you to pick?
2. Whom are you playing?
3. Do they provide access to books/databases etc or are you on your own?
4. Can you write down your games?
Follow up questions can be provided by other members.
Better still play the Classical and you have the choice to go into lines of either the Najdorf or the Dragon, depending on what white does.
The dragon, as "fearsome" as it is among amateur players, is actually the safe choice for the super GM, as with best play it typically leads to advantageous, although only marginally, endgames for white, which black can usually hold. in games betwen two 2700+ players, %60 of dragon games are drawn, compared to just %46 of Najdorf games, and black only wins %17.8 with the dragon, while that rises to %22.3 with the Najdorf.
Thats funny, because I heard somewhere (probably from Fischer) that 9/10 games in the Dragon are won by White, not drawn.
I'm not sure why, but you deleted part of my comment in your "quote" - the part that referenced the chesstempo database as my source. Anyway, Fischer thought beating the dragon was as easy as "Sac, sac mate" (that might not be the exact quote, but it's about right), but he never said that 9/10 games are won by white. I'm not sure who told you that 9/10 dragon games are won by white, but I don't think it's true at any level of play. The highest percentage of white wins I see in any database (this is from ChessBase Mega 2011) is %42.5, and that is among players of any rating. Anyway, "9/10" just sounds like another case of exaggerated gossip.
No witty comments about the Dragadorf? Anybody?
I started to beat him up but a cop Dragged me dorf?
In your opinion, if you were forced to play Sicilian hypothetically every time, would you play the Najdorf or the Dragon more frequently and why.
Please try to be clear and instead of long posts condense the main points :)
Thanks!!!!