[quote name='Beedster' timestamp='1422285671' post='2670667']
Makes a difference on some basses and not on others. As has been said above it should be kept in mind that 'difference' does not always mean 'improvement'. Some bridges are an improvement simply because they allow better intonation, alignment or action, others because they link the surfaces better than the original perhaps allowing more sustain (or fewer energy losses), others because they actually do alter the tone. Either way, there's a whole lot of reasons why you'd change a bridge, but I've done it many times and I'd say that tonally there are often as many improvements going from a heavy and expensive bridge like a Badass II to a Fender BBOT as there are the opposite direction. A very good example for me is my 4003, on which the brass Hipshot version bridge to my mind takes something away from the Ric tone and sustain, despite facilitating far better intonation and string alignment.
I'm sure the answer to the OP's question is quite simple, you'll never know until you try a certain bridge on a certain bass.
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I think Chris sums it all up best with this. However, I'm still of the opinion that you're unlikely, on average, to gain anything from swapping bridges.