There is varying opinions on this subject but in the end it comes down to preference, what is best when you are mowing your lawn, what’s best for your lawn and what outcome you are trying to achieve.
When mowing the lawn, if your grass is kept nice and low and mowed weekly then not bagged is a great option it means you will be able to mow your lawn faster and have less trips emptying your grass clippings, the mulched clippings will work to feed your lawn throughout the growing months, however if your grass grows too high and you haven’t mowed it weekly then this won’t work as well, you will be in this case leaving clumps that can yellow off your lawn and suffocate growth in those patches. All in all, if your lawn is maintained often then not bagged is a great choice.
If you are going for a more premium and cleaner look, then catching your clippings is the way to go. This will leave your lawn looking fantastic and allows your grass to grow consistently, if you have let your grass go for a few weeks through summer or coming out of the colder months of the year and it is overgrown then bagging is a must but it will take considerably longer as you will be emptying your bag more often.
Lawns like to be fed and a reasonable amount of your mulched clippings dressed back over your lawn every time you mow is a cheap and effective way to do this, my preference as a home owner and a lawncare professional is to have a balanced mix of bagged and unbagged, ideally the first mow on a new property or coming out of winter I would always use bagged but during summer with consistent weekly mows, I would likely go a mix week for week of bagged then unbagged but in the end it comes down to preference, just tell us how you want your lawn done and we will be more than happy to give you the look you want.