I used Mr. Car Shipper to move a car (daily driver SUV) from the east coast to the northern rockies in the summer of '21. Cost was around $2,250 and while I wasn't overwhelmed to the upside with the experience they did exactly what they said they would and there were no issues.
The shippers will insist on the car being relatively empty so you can't move much by way of personal goods if you ship. The process also took almost a month from drop off at origin to pickup at destination, so if you need a car in the interim you'll need to rent.
Lastly, don't forget to pull your EZ Pass / auto toll beacon out of the car before shipping or you'll get a couple of hundred dollar toll bill as the truck passes through each reader.
I've done the cross country trek 3 times in the last 3 years. I think it comes down to your time and how painful you find long drives, plus whether you need to bring a bunch of stuff with you. Driving does also give you a little flexibility for your departure date/time vs. an airline ticket.
