Both exports use the existing Work Orders → Export permission — the same one that controls the work order PDF. Users without it do not see any of the three export options; the work order itself stays visible to them.
There is one additional rule. If your account has hide mechanic labor rates and costs switched on, under Settings → Admin settings → Labor rates, mechanics do not see the quote and invoice exports at all — on the list, on the work order or on mobile. These documents show labor rates and totals, so they are hidden completely rather than partly redacted.