Lovely axe!

Beef tallow may seem like a nice fat to use & it's probably great for your palm skin but it doesn't offer the greatest protection for your axe handle.

Beef tallow is very stable & won't easily oxidize.

Boiled linseed oil is unstable & oxidises rapidly in air. This forms a hard barrier on wood and projects it from the elements. Just watch out because it can cause rags burst into flames as the oil oxidises.

Seed oils are great for wood but you don't want them in your blood stream or body fat.