After the first few moves, all 8 minor pieces are valued slightly differently. It's useful during a game to be aware of which minor pieces are the best for each player, and to pay attention to when these values change as the game goes on.
Trying to talk about small difference in value without a position is pointless. You do say the starting position, but that's (obviously) a position that is about to change very quickly with many options for both players.
This is not a simple explanation.
The exact answer depends on the situation of the game, however by and large the following principles apply. However know that there are lots and lots of exceptions.
1) Generally speaking Knights enjoy closed positions. In closed positions knights are the key to unlocking the position. Bishops don't enjoy closed positions. In open positions Bishops definitely are more at ease, however Knights are not exactly nullified in open positions.
2) Bishops enjoy the benefit of range. Think of a knight like a knife and a bishop like a gun. Both are lethal if used right, but you need to be close to the target to use the knife. It is the same with knight, they have limited reach. A bishop on the other hand could affect play even from far.
3) However Bishops are handicapped by being restricted to just one color boxes. For example a Bishop on light colored boxes is completely powerless against pieces on dark boxes. So you could place a pawn on light boxes and know that the opponents dark box bishop cannot touch it.
A Knight on the other hand covers all squares, unlike a bishop which has no influence on half the board. This would seemingly give knight a lot of power, but Knights are fragile, in the sense that you could attack a knight and if it has to move then it loses control over whatever boxes it was controlling earlier.
That is to say that suppose a pawn is about to promote and you are protecting the promotion box with your knight. Now if you knight is attacked and needs to move then you lose control over that box. However a bishop could move and still continue to protect the square.
So as you see both Knight and Bishops have + and -. Which of the two is more useful to you depends on you using them in such a way that their limitations are not exploited and their advantages are most enhanced.
However it is generally agreed that a pair of bishops is slightly better than a pair of knights as the two bishops combined could exert influence over the entire board especially. However that is just one part of the story.
I did word the initial post very vaguely. I do actually understand the influence that the changing dynamics of the position have on the way that each of the pieces work.
Thank you all for the reinforcement of that though.
I think I was just trying to work out whether there is any difference in the pre-game, but as there is no real position, it does not matter.
One situation where a knight is far more valuable than a bishop. If you are down to a few pawns, a knight can be far more valuable than a bishop, Although the knight is much slower it can reach all 64 squares whereas a bishop can work only the 32 squares of one color (32 white squares or else 32 dark squares). If your opponent has only his white square bishop and you can move most of your pawns to the dark squares, you have a substantial advantage in being able to reach all your opponent's pawns whereas your opponent can get your pawns only with his king.
Both are given the value of 3 points, but it is common knowledge that the bishop is generally more valuable than a knight. However, there are some situations where a knight is better.
In your opinion, how much of a difference is there between the value of the minor pieces at the beginning of a game?