It depends on the situations. If you reach the cap for gunners, additional experts or vets are not very useful. Similarly, if you reach the cap of repair (280/s repair), additional experts and vets for repairmans are not useful. The only ships need a lot of vets are cv and ss (fighters in cv and all sailors in ss).
If you are talking about ships in blizz, engineers and repairs do not do much so gunners are the sailors you want to put experts on first.
With the event, it is easy to get to the first 40 vets by converting/rolling. Then, the success rate decreases dramatically until around 100 vet. Then, beyond 100 vet is more difficult. Use your vet items only between 40-100 vet (or closer to 100).
Also, your gain in experts each game decreases with the number of experts on your sailors. If you are leveling your sailors, leave some rooms for expert gains (i.e., do not fill up your sailor with full experts).