I think the reverse is true: The extraneous background light (ambient or from
other fluorochromes) should have a fairly flat spectrum over the width of the
filter relative to the strongly peaked specific fluorescence. The
*background* will therefore increase roughly proportional to the increased
filter bandwidth. At the same time, the *signal* will not increase
significantly once the bandwidth is wider than the spectral peak. Thus, as
the bandwidth *increases* the signal-to-background *decreases*.
One may then argue that the best signal-to-background will come from the
*narrowest* bandpass filter, centered right on the spectral peak, but the
problem there is that, if the band is too narrow, the total detected light
signal will be very low (and you would usually be looking for improved
signal-to-background exactly because your fluorescence levels were low to
begin with). When the detected light level is low, other sources of noise
(electronic) become more significant and the problem of photon counting
statistics arises.
These days, I would be inclined to trust the manufacturers to select the best
filters if they have each been specified for the fluorochromes you are using.
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