Use the search feature to find threads on this topic. It has been discussed, debated, argued, .... over, over and over again. After you read many threads, you will have to arrive at your own conclusion. "Popular" as your question asks is not the right question, rather what you want/need to do, how you wish to work, how you wish to be paid, what kinds of customers and their demands, what kind of equipment you wish to invest, etc. You will see from existing threads opinions range widely. There may be firm answers to some questions, but this question isn't one of those.
I may have replied to this before , but , I only mulch . I use an 48" Exmark Metro and installed the mulching plate and baffle . Its a little tough in the spring with thick juicy grass . No discharge , no debris in beds or on cars etc....... It does require constant cleaning to maintain peak performance .
I started out in 2002 Bagging with a Craftsman. I have since moved up to a 60" Exmark with the 3 bin bagger. This year however I have cut out 75% of my bagging with a 31 hp Lazer Z XS mulching. To make a long story short I can mulch 75% of the time, but when the leaves are knee high, Thank God for my bagger (After I have mulched them of course)
I mulch my lawns for now but have been entertaining the thought of gettin a bagging system. IMO, customers probably prefer bagging grass even though they cant tell the difference. With a bagging system I could prolly get paid more green.