I use the universal 5 gallon bucket since the beginning of time and have no intent on changing, it has served me well for holding tools, doubling as an emergency water catcher, step ladder and seat..none of that you can do with those containers.....
....Also with the bag I tended to throw alot of random stuff from the jobs in there and not get it out again .....
I also use buckets with my toolbag. If I am going to unclog a sink I will throw my small bucket, a trap, my drill, my short snake, 4x5 drop cloth, towel, and probably my kneeling pad into a bucket. Grab that and my tool bag. Keeps my weight more even on both sides so it's easier on my back, I have the bucket to throw crap in, and it cuts down on the trips I make to the van. The customer is also impressed that I somehow knew what I would need before even seeing the issue with my own two eye balls.
Then if I make another trip out for say a tailpiece, extension, putty, caulk, it all goes in another bucket. Makes packing out real easy and the customer can help if they want which most do although I try to get them not to. I appreciate the thought but I would really rather do it on my own. At least with the bucket system they aren't carrying things in their arms and coming to my van to put stuff in, they can just set the bucket outside the house door.
As for using a bucket to catch water, my toolbags have plastic bottoms so at times I will use my toolbag to catch water and I get to see this hilarious look on the customers face :vs_shocked: It's really great when they see I will need a small bucket and they offer one but I turn it down, they think I have some special plumber technique. I disconnect a supply line and pour the water in my tool bag. It's like something straight out of abott and costello!!! lolz