There are advantages in using a separate USB chip, and letting the AVR communicate via its UART.
A USB stack has to respond to polling from the host PC. This happens at least every millisecond. That means that it is even more difficult to guarantee hard real-time response to events, as the MCU might get interrupted to respond to the hosts USB poll.
When there is nothing to communicate, or the MCU wants to focus fully on a real-time task, it still has to respond to some host USB polling events, or the host will 'lose' the device. So it is hard to ignore. A dedicated USB chip, like an FTDI offloads those tasks from the AVR.
A small issue is the USB stack will consume a reasonable amount of flash memory and RAM, so the chip needs more resources than a simple AVR.
Also, the two parts can be separated onto two boards, so the USB isn't a fixed cost, but might be shared across multiple boards.
On the converse side, the major benefit of using an AVR with a built in USB peripheral and USB stack is there is only one part to buy, and assemble.
I have not checked recently, but I believe the newer FTDI chips provided a higher USB data transfer rate than the AVR's USB. However, AVR UARTs were so slow that an AVR with USB is faster transfer than the combination of FTDI (or any USB interface) communicating via the AVR's UART because of the slow AVR UART.
Edit: FTDI do make other interfaces than UART. For example SPI. I have no experience using them. Some AVR's do support 9 (maybe 12) megabit SPI transfer. The FTDI is the SPI master, which isn't ideal. If the AVR is transmitting, it might be fine.as the FTDI's do have buffers, but receiving might be 'like drinking from a fire-hose'. AFAIK, you'll have to do work on the host PC to get it to work.
The highest speed transfer might be via an 100mbits Ethernet daughterboard, but I have not seen measurements of throughput.
I am happy to use other microcontrollers than AVR. So I might use something with a fast UART and a DMA controller which could move characters without CPU involvement. If that is a useful approach, maybe look at the the Arduin Due, or the mbed, the ST mbed is called nucelo which is low-cost.