I do not lift barbells. Too high a risk of injury for me.
I use free weights occasionally for curls or shoulder side to side or whatever it is called. I use them for a one arm bench row. I have done a bench deadlift with them.
I stand on a resistance band and do biceps curls. Also, I have a resistance band rapped around a support beam in my basement and do a paloof press. I counter that with a rear delt fly with the band around the beam to counter the pushing out of the paloof. I use a 2 handle core ball for chest presses or stand with my back to the beam and push out with a band.
As the trainer pointed out, with the appropriate resistance levels of the bands, you can replicate almost anything you do with weights. You can Google this on Livestrong.com.
When I went to the gym, I did the seated cable weighted lat pulldowns and rows. Now, I kneel on a pad and with the bands looped through the door anchor at the top of the door, I do a triceps pull and moving away after that, I do a lat pulldown. Similar resistance feel to the cable weighted machine.
With the TRX over my door, I do rows and a combo squat row. This is a body weight exercise developed by a navy seal. Also, I stand on a platform and with a rolldown device called the "wrist blaster," I work on the arm and forearm strength and I slowly unravel the blaster and then slowly bring it back up.
I guess it depends on your objectives. It depends on what you like, what works for you, and what minimizes the risk of injury.