It should be quicker overall:
1) Customers no longer get confused with pay/collect lanes that some did before the ticket system, and bumping into each other when the lines get too long.
2) In the older single order/collect lane system, if customer A is ordering, customer B behind used to wait for A's order to come first, before his order will be taken. It is likely the bottleneck harder for Mac to control is ordering, given how some folks either order a huge party size or they have 101 questions about the orders.
3) Less travel time for order staff as they just key in orders, the staff travel internally to pick the orders as the food items slide into the "collection chute". The Macs at where I live have streamlined the assembly to be perpendicular to the counter, all the packed burgers/wings go thru the single chute for collection.
4) Optimized drinks dispensing. One dude manages the drinks full time when the order piles up, he actually places them onto a counter that is divided into the various drinks. (coke/coke zero/etc). No need to refer to the funky push in tab on the lid.
4) Fries is handled by the dedicated order picker. He/she collects all the required food items and then collects the fries LAST, making sure it is hot for the customer before she hits the ticket number as ready.
I see the whole process as much more scalable to volume and time efficient. Only issue is the staff have to scream the numbers out like the neighbourhood bubble tea store. It makes it worse when some of my branches have self-order kiosks, which product 4 digit numbers instead of three digits from the staffed order counters.