Best soffit vent w/ anti-backdraft, for bathroom vent fan?

The fans in the bathrooms are breaking down so time to replace them & also vent them to the outside. Don't want winter wind to suck open the flapper and pull warm air out of the house.

 

There should be a flapper in the adapter where the air exits the fan bousing.
There should be another flapper in the vent where the air exits the house - either wall or roof .
There won't be much heat loss if you have both.
Not sure what you mean breaking down.
If you are satisfied with your existing fans but the motor is wearing out or getting noisy you can usually oil the bearings in the motor and get a bunch more years out of one.
Otherwise you can usually buy a new motor that fits. Bring your old one to your local Grainger store and have them match it up.

 

My exhaust grill has a little flap on the side for a back draft damper as Lanachurner says.
Here is a 4"back-draft damper you can add:
http://www.supplyhouse.com/Fantech-RSK4-RSK-Series-4-Duct-Backdraft-Damper

When my cheap fan stopped working I installed an in-line fantech fan in the exhaust line up in the attic and plugged it into the old housing. It was a very easy install and the fan is almost silent.
http://www.supplyhouse.com/pex/control/search/~SEARCH_STRING=inline fan

 

The backdraft damper is a good idea. I'll probably need a short length of flex hose to get everything lined up. Those inline fans are as expensive as a whole new fan/light assembly !

I don't want the damper on the soffet vent itself; wind can pull it open and suck the hot air out of the house. Also bugs etc can block it easier than something deep in the system.

 

I don't like to vent a bathroom through a soffit...hot/moist air will want to rise, and depending on where you live, condense on the horizontal surface, and if the soffit is venting the roof, come back inside and condense there as well. They work better through a sidewall or up through the roof.