Both are certified to TIA-568 and both carry gigabit to 100 metres. The difference is headroom. Cat6A carries 10 gigabit to 100 metres; Cat6 manages it only to about 55 metres and only with care. Newer Wi-Fi 6E and Wi-Fi 7 access points, and the switches behind them, increasingly want 2.5 or 5 gigabit uplinks that Cat6 cannot reliably provide.
Cost difference at the point of installation is modest, typically 15 to 25 percent on the cable and terminations, because labour is the same. Rework after the fact is not modest: pulling new cable through a finished ceiling costs more than the whole original job.
Our recommendation for an office fit-out: Cat6A to every access point location, every meeting room and the comms-room backbone. Cat6 is acceptable to ordinary desks that will only ever host a laptop dock. Fibre between floors.
Whatever you choose, insist on three things: installation in containment, labelling at both ends, and a certified test result for every link. The test report is the only proof the installer did the job to standard, and the only thing a future tenant, landlord or insurer will ask for.