I've always wondered, what are the main tactical and strategic differences between Rad1 and Rfd1 (or Rad8 and Rfd8 as black)? I know it's a subtlety, but my guess is there are some common principles that apply often.
When you move one rook to the center, the other rook, obviously, cannot cross it. If you play Rfd1, you cannot then play Rae1. And if you play Rad1, you cannot then play Rfc1. So, part of this decision is planning ahead and thinking about which other file you are likely to want a rook on.
Relatedly, if you play a move like Rae1, you are trapping your f-rook, often making it vulnerable to an attack from the bishop. Be careful before playing a move like that.
If the opponent has a bishop on g7, it is sometimes a good idea to get the rook off of the a1 square, especially if the center is not closed. This allows you to more easily play b3 or b4 without putting your rook in danger from the bishop.
Normally, when I need to choose between one of my rooks, whether to move on a promising center column or to defend a center pawn, I wonder myself which side columns are better.
If there is not a task to do on queenside's columns, I move the a-rook. The f-file rook, which is the h-file rook after castling, is used to better protect the castled king, as well as to provide support to f4 if a7-g1 diagonal is not controlled by a black bishop.
Sometimes, moving the f-file rook is indeed not recommendable because f2 might need the f-file rook as a defender.
Cases where I move my f-file rook are mostly related with plans of playing Rab1 or Rac1, with no troubles for my castled king. Additionally, as @DM noted, if it is Rae1, the needed move, the f-file rook gets trapped.
It comes down to what squares you want your rooks to be on, which in turn is driven by strategical considerations for where your rooks are going to be most active. In general you want your rooks to be on open files (files in which there are no pawns of either color), or semi-open files (files with an enemy pawn but not one of your own) if open files are not available. Of course this is abstract, so let's take a concrete example.
[FEN ""] 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3
This is the starting point of a myriad possibilities in the open Sicilian. If we just proceed from here then it should be clear that Black wants a rook on the c-file while White wants a rook on the d-file. This is because those are their respective semi-open files. A rook on c8 for example would control four squares (c7, c6, c5, c4) and is also instrumental in the iconic Sicilian exchange sacrifice ...Rxc3. For the other Rook, Black wants it on the d-file to support the standard Sicilian equalizing break ...d5, while White would prefer the e-file since 1) the Rook controls most squares there and 2) the pawn push e5 is a standard attacking idea.
Therefore in the Sicilian, Black is probably not playing ...Rad8 because he is playing ...Rac8 and ...Rfd8, while White is probably playing Rad1 and Rfe1.
However, a lot of this is going to depend on the position. Let's take this position and add a few more moves:
[FEN ""] 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 g6 6. Be3 Bg7 7. f3 O-O 8. Qd2 Nc6 9. Bc4 Bd7 10. O-O-O
Now we are in a Sicilian Dragon, Yugoslav attack. This is a sharp line where both sides are looking to attack the other's king. Black still wants a Rook on c8, and maybe on d8 as well (although doubling on the c-file is also a real possibility), but White no longer wants his Rooks on d1 and e1. Instead, White wants his rooks on g1 and h1 to support pawn pushes against the Black king. Rooks on d1 and e1 is no longer effective because in this pawn structure, White's active plan is going to involve pawn advances on the kingside and rooks on these two squares don't contribute to that plan.
So: it comes down to where you want your rooks to be, which in turn comes down to the specifics of the position.