This is not the typical debate of which is worth more.

Quite by chance, my son came up with an interesting experiment to perhaps answer this question, or at least clarify it some.  He asked, "What would it be like if one player had all four Knights, and the other had all four Bishops?"

I said I didn't know, so we tried it.

I figured in fairness, a good rule would be for one player to choose which pieces he wants, and other plays white to go first.

It was certainly an interesting game, and quite difficult for both sides. Has anyone ever tried this variation?  If you're willing to give it a try, it would be interesting to read about your results and observations.

I came up with this before, but someone told me there's no point in conducting this because the bishops would win every time in this situation ?!

Are the mathmatics of the situation=  whichever piece has more available squares becomes the most effective.  In an entirely closed postion the bishops lose a great deal of effectiveness bc pawns block their squares keeping the number of available squares to move few.  Knights will never have more than 8 available squares ( the max of their movement), bishops can have at the most 13 available squares.    Therefore, 4 bishops to 4 knights would have 20 more sqaures available to move.  Making the bishops far more active.    If you were a great player playing the knights, you would want to trade off two bishops of the same color giving your opponent a weak color all over the board.

I am not sure if I am correct but am curious how the analysis would work?

As a practial matter it seems to me that for the most part the stronger player will win regardless of who has which sets of minor pieces.   All other things being equal I'd have to imagine that the Bishops would have the strongest chances because of their range.  I think with the side with  Bishops could happily sacrifice a pawn or more to open up lines in the opening or middle game and really reak havoc with those bishops.  I don't think there would be much the knights could do against this.  I think given that fact it would be really hard to force the game to be a "closed" one that would allow the knights to be equal or even superior.  

I agree with poly...what are the knights going do if the bishops seel off all the squars the can go to?  Exactly! NOTHING!!!  The knights are going to do nothing if the bishops seel off all the squares!

I have to agree with poly as well. Keeping the game closed is nearly impossible if the bishop side is ready to scarifice a few pawns. However, the knights are much quicker to develop.

It'd Be Equal....