Ridgid is really the only way to go especially over long runs. We usually spec 4" sched. 20 PVC pipe as it comes in longer lengths than 4" metal does around here , though elbows can be tough to source sometimes. Unfortunately most contractors / HVAC guys will use flexible corrugated hose because it's cheap and fast. If it's a luxury project they'll splurge for the flex aluminum instead of the plastic kind. This type of pipe can cut a fan' effectiveness in half over long runs. Little thought is really given to these fans in most homes today. They are often undersized for a given bathroom and poorly located too. The crappy pipe detailing makes a bad situation worse. Panasonic's website has (or used to) a pretty good tutorial on how to properly size a fan, where to locate it and how to properly pipe it to the outside. I think much of the problem is cost and ignorance. Most people know you get a fan in your bath , but when pressed they won't really be able to tell you its there to expel warm moist air from your home, not smells. They assume that the $34.95 version will be fine for them and a quick & dirty install will get ya out the door for a hundred bucks. The reality is, many master baths, and some hard working kids baths need a much larger fan than 35 bucks can buy. We are often talking $100-$200 for an adequate model, more if you want features or quietness. Add the increased piping cost and labor for the proper venting needed on higher capacity fans and this can quickly become a $500 line item - which starts to look crazy for something as pedestrian looking as a bath fan. Timer switches are also a very good idea as most fans even properly sized ones need to run a while after you've left the bath to completely exhaust the moist air.

Some of my info will repeat what has already been written. In the first photo: It looks like the duct is looped around to go behind the fan and then it goes up to the roof to exhaust. I would have rotated the installation of the fan housing itself to give a shorter path to the exhaust boot. 2) Rigid duct is better than flex duct. The wire coil in the flex offers more resistance to air movement through the duct resulting in your fan moving less air. 3) Insulate the duct for less chance of moisture vapor in the duct condensing and pooling in the duct, or running back into the fan housing. 4) It looks like light can be seen coming from the bathroom below. If so, the fan housing installation is poorly sealed to the bathroom below. Seal those gaps/holes, either with canned foam or aluminum tape, etc. Free air movement between conditioned living space and unconditioned space is bad for myriad reasons. See the dark/discolored/dirty fiberglass insulation? That discoloration is usually a result of the fiberglass insulation acting as an air filter. The discoloration is from the fiberglass filtering pollutants put of the air as air flows through the fiberglass. The second fan: Comments remain the same, with one addition. Since the duct is longer, when you replace it with rigid duct, have the duct leave the fan and run it vertical to a height a couple of inches above the height of the gable wall's exhaust boot. Then as it runs horizontal to the exhaust boot, pitch the duct downward a bit. That way if there is any condensation in the duct, it'll run out versus pooling in the duct.

The installation of the bathroom exhaust is a big problem, but not your only problem. The overarching issue is that your kitchen exhaust is from the ceiling rather than a hood over the range/cooktop. Trying to work with an existing ceiling exhaust, even if you replace it with a correct ceiling exhaust, well, it's still a ceiling exhaust. Take this opportunity of your kitchen reno to improve this arrangement. Lots of problems with a ceiling exhaust, most notably: (1) too much opportunity for grease and smoke to escape to the rest of kitchen, (2) difficult to clean at the ceiling, (3) not enough cfms to pull the smoke and grease from such a distance, and (4) no canopy shape (as a hood would have) to corral the grease and smoke. Take the opportunity of your reno to install a correct hood exhaust. Edited to add: I just noticed you said you are in a condo. If you are stuck with that exhaust location, you can still install an "island hood" in a chimney style that meets the ceiling where the duct is located. Make sure the hood is in a canopy shape, and is 6" wider than the width of the cooktop.

Comments from us will do nothing to change thigs. You need to go up into the attic and look to see what they did.