Here are my quick notes on replacing noisy contractor grade fans in bathrooms. The Broan 688 and variants are common installations in new and rehabbed homes because they're relatively cheap. But boy, at 4 sones sound output, they're very loud and irritating to leave running for a long time.
The Broan 688 is very small, which limits your choices if you're retrofitting an upgrade without cutting out a bigger hole in your drywall. The dimensions are basically 7.25" square, with a 3" round duct, and moves 50CFM of air. A lot of installs with long runs use 4" ducts, so you may have an adapter inside your ceiling as well, to connect this. On the plus side, these fans are very low-profile, so you don't need much height going up into your ceiling to fit them.
Here were my upgrade options, ordered in terms of increasing difficulty and quality. I picked the same low-profile ones so that I could fit them without difficulty between my joists. If you have 8" joists, you could probably go with something cheaper that are not low-profile.
Upgrade kit specifically designed for the Broan:
This kit allows you to replace the fan without having to remove the housing that's screwed into your ceiling joist, or rewiring the electrical connections. Just unscrew the old fan, disconnect the plug, and then remove it, and screw in the upgrade and connect the plug. Very easy, but from reviews (like this one ), it didn't seem that quiet at 3 sones, since you're just reducing the sound output by about 25%.
Fan with 50CFM that's an exact fit for the ceiling cavity:
This fan will let you use the same ceiling cavity (no need to cut out more drywall), and it's much quieter at 1 sone. This is the one that I went with for one of my bathrooms, that worked really well. It does require that you remove the old enclosure and rewire the power, but the good news is that the location of the vent, mounting screws, and wiring inlets are almost identical to the Broan you're replacing, so there's a very good chance you won't be in for any surprises during the install.
This measures right around 60dB in operation.
A slightly higher 70CFM replacement that's the same dimensions as the previous one but louder at 2 sones:
An even quieter option per unit volume are the Panasonic WhisperFit options, like the 80CFM below, rated at 0.8 sones:
This one has a much larger footprint (almost 12" square cutout, and 5.5" up into the ceiling), and slightly different locations for wiring and vents (this has a 4" duct, but comes with a 3" adapter). I spent much more time installing this one in my main bathroom, but was happy in the end at the amount of air moved for the same sound (80CFM vs 50CFM against the Delta Slim Breez for the same 60 decibels).
Keep in mind that if you don't have anough clearance in your ceiling, you may have to go with an even slimmer version of this called Panasonic FV-10VS3 that is < 3.5" in height, but will require an oval to round duct adapter.