How long ago did you add the yeast and what temperature was it added at? If it was too high (like if you had just boiled it) the yeast could have been killed off, too low (like if the juice was fresh out of the fridge) and it may take longer or be inactive until it warms up.

Was the yeast from the same packet for both bottles? Could be that the one added to the apple and mango was largely inactive. Depends what kind of yeast it was too. Normal off the shelf baker's yeast can be slow to start apparently and is prone to having a lot of dead yeast.

Just juice or did you add sugar? The natural sugar content of both juices should be relatively similar (though without added sugar the result is likely to be pretty low ABV) but the yeast might be able to get to work faster in orange juice due to how these sugars are distributed between glucose, fructose and sucrose. I know some take longer than others to ferment.

Did you add any yeast nutrient or something to help it along (raisins are a common one I see people mention)? I would expect mango and apple to have a better variety of nutrients than just orange but if it is struggling for some reason it might help.

Are both the bottles being kept together so they are about the same temperature now? I had one bottle slightly nearer my computer than the other and it got to work a couple hours sooner than the other did just from the extra heat coming out the back.

Lots of little factors could result in a difference between them. If it has only been a few days though then it might start up randomly later. If not you could try adding more yeast if it still isn't doing anything in a few days, plus the existing yeast if it is dead can provide nutrients for the new yeast.