What are the parts of your current rig?
Will you also need to take a monitor and keyboard?
Packed well, either overhead or in luggage can be ok.
I have done both.
Not with a monitor, though.
A monitor is what is likely to get damaged most.
Consider that some airlines may require you to store overhead baggage in the cargo hold due to limited overhead space.
First class passengers would not be subject to that.
Taking a laptop might be the best solution.
If you want small and portable, look at the Lian-li TU150 ITX case.
TU150 use of a tempered glass main panel means a modern internal aesthetic along with proper masking to hide internal cabling. Another neat cable management trick is that Lian Li allows the top panel where the handle recesses to hide wiring as well.
lian-li.com