Let us know which way you think is better, ponchit.
I used to use the paper towel/bag/refrigerator method. All herbs lasted about a week, but parsley tended to get slimy and the others tended to brown or yellow, so I'd toss a lot.
Then I used the water/vase/refrigerator, method for parsley. If I didn't dump the thing over, the parsley lasted at least 2 weeks.
Now I use the water/vase thing on the window sill. Much better. Stuff lasts a week, I see it, change the water all the time, and use it more often. When I put basil stems in the water on the sill, it grows water roots and lasts until I use it all.