Is there a difference between how long fresh herbs and vegetables last if they are in a plastic bag or in the open? If it does, is there a break-down of which ones it does make a difference for - example: cilantro seems to get mushy very quickly in a bag but last for a week in the open, but scallions last much longer in a plastic bag and deflate almost immediately in the open.
It depends on the moisture content. If the vegetables are wet when put in they will get mildew and go soft faster because the water has no place to evaporate. This is made worse when leafy greens are put in bags since they have so many nooks and crannies to hold water, and they seep out their own moisture content because of the large surface area. Try drying off the veggies first or putting them through a salad spinner to get as much water out of them as possible.
The optimal temperature for storing herbs is about 12 degrees Celsius, which is about 55 degrees Farenheit (53.6 actually).
If your counter top or pantry are near this temperature, then you shouldn't refrigerate your fresh herbs. If you must refrigerate them, they will give off moisture which will condense on the leaves and make them less fun. You can use a paper towel or such to capture the moisture so that it doesn't condense, but the leaves are still losing their moisture, making them less crunchy/upright and causing them either to wil or dry out completely.
Ultimately, the best is to just use them fresh.