Which side to castle in the Sicilian Defense?

You should castle on the opposite side when at least one of the following factors is true:

1. When you are up in development and your opponent has already castled, you should consider castling in the opposite side. That way you will have a clear game plan and will also be able to capitalize on your development advantage.
2. When you have a damaged pawn structure (doubled paws, missing pawns, far advanced pawns, etc.) on one of the sides you should consider castling on the other side.
3. When opponent’s pieces are especially active on one side of the board, it is usually best to castle on the opposite side.
4. If you want to complicate the game you may consider this option. That may be true if you must play for a win due to a tournament situation, when the draw is not enough. Also that maybe done when you're playing against a stronger opponent, who is much better in simple/technical positions. That maybe your best bet.

You should not castle on the opposite sides when at least one of the following factors in true:

1. When you are behind in development and you need extra time to develop your pieces, it is usually not a good idea to give your opponent a straight forward way of launching an attack.
2. When the opponent’s pawns are advanced towards the side you’re about to castle, it is not a good idea to castle there (especially if the opponent’s king is castled on the opposite side). It will just give him a positional edge in the attack.
3. When there are open/semi-open files in-front of the side you’re about to castle, you should probably reconsider your decision to castle there (especially if your opponent has castled on the other side). That will give him more attacking possibilities, such as rook lifts, various sacrifices, doubling of pieces on the file, etc.
4. If you playing against a weaker opponent you may want to avoid castling opposite sides, in order to avoid sharp game and keep everything under control.

Note: These are general rules, not laws, meaning that there are always exceptions to them. When you’re making a decision what side to castle you should always take your time and evaluate all “pros” and “cons” and base your decision upon your own analysis. This is a very important decision. It pretty much dictates which way the game will continue. Take your time and think twice.

Good explanation by IMBacon. 

Thank You Sir!

Also, in the Sicilian (in particular) it is often useful to delay castling until your counter-play is well under way and your opponent is too busy to launch an immediate attack on your castled position. It's not too uncommon for the Black King to remain in the center for 25 or 30 moves... or even to give up castling entirely.

I could post a couple of illustrative games if you wanted to see them.

Here's one where I played Black in the Sicilian Najdorf, and castled on move 27 (after my counter-play was already rolling):

https://www.chess.com/daily/game/90890754

The other game is an old OTB (over-the-board) tournament game that I played about 40 years ago. Black never does manage to castle

:

Here's another where I just don't manage to castle, also with notes:

https://www.chess.com/forum/view/game-showcase/a-heroic-defense-in-the-sicilian-najdorf-kids-dont-try-this-at-home

Indeed. Both of the above posters are very on point. To answer your question directly though: Kingside in most Sicilian systems, as counterplay is often directed toward the Queenside & Center. Best wishes

I almost never go over my games with a computer. Engines don't explain anything. They don't have ideas, only calculations. 

From a human point of view, Rxf3 is the superior move because:

1) it is more forcing than Bxg4

2) it reserves the e6-Bishop to attack the enemy King once he flees to h3.

I'm afraid that this comment is the tip-off.

The two lines (Rxf3 and Bxg4) ONLY transpose if the sacrifice is declined. Stockfish at search-depths of 20 ply or more will decline the sacrifice, no matter whether you start with Bxg4 or with Rxf3. Then the two lines merge and the evaluation is basically identical.

But what does this have to do with "the human point of view"?

"The human point of view" does NOT consist of putting the position into an engine, letting it crunch the numbers, and then reading the evaluation off the computer screen. In fact, you will get banned if you do that during the game. You are supposed to do the calculation YOURSELF, in your head.

Since White is clearly lost if he declines the sacrifice (and I'm sure Stockfish will confirm this), then when a human (as opposed to an engine) is doing the calculation his #1 concern will be what happens if the opponent ACCEPTS the sacrifice. And in that case, there is no transposition, and the Rxf3 line is far easier to calculate, since when the enemy King flees to h3 the fact that you still have a Bishop on e6 (instead of having already sacrificed it) makes the follow-up attack crystal-clear.

The fact that you claimed that the two lines transpose tells me unmistakably that you are just looking at engine analysis, not trying to figure it out yourself. Bear in mind that engine assistance is not allowed in daily games.

So I have zero confidence in your claim that "From a human point of view, neither is superior to the other." 

What you really mean is: "From an engine-user's point of view, neither is superior to the other".

If you’re opponent has an open C file which they usually do if you’re playing against the Sicilian as white you typically want to castle kingside so as not to have a rook staring down an open file directly at your king

Oh you meant as black. Disregard my comment