freeze branding or tattooing??

No downside to tattooing. Zero recovery and a very simple do it yourself process.

Freezebranding a very underutilized tool. Needs to be someone that has experience or can look ugly for life. Alot if variables and wouldn't recommend trying yourself for the first couple times. But a great tool non the less. Just make sure you plan on keeping the dog forever ....or everybody will have your brand running around visibly.

Prices range on branding.
$10 buck to $35 a piece is what I have seen lately.

Might also consider paint branding as well. Very cheap, visible and temporary and can do it yourself.