There are a few units in the game which have a significant portion of their HP in shields. This leads to them getting shafted in terms of the HP boost they get from vet, as the shield HP isn't taken into account.

For example, Obsidians have 2,750 combined HP to Ilshies' 2,500, but they only get 125 HP per vet compared to Ilshies' 250. This means that at 3 vet and above Ilshies have more HP than Obsidians do.

Fatboys suffer from a similar problem. At 32,500 combined health, they get a paltry 6k extra for full veterancy, whereas A Neptune starting out at 25k damn near catches up with 37,500 at full vet.

So I think the following units should have their veterancy HP buffs take into account their shield HP, not just the base HP:

  • Obsidian
  • Harbinger
  • Czar
  • Titan
  • Continental
  • Fatboy

No changes need to be made for shield generators as these cannot gain veterancy anyway.

"Why shouldn't the shields get extra HP instead?"
Even assuming this is possible, shield health isn't visible to opponents, so would be much more difficult to account for if it changed with veterancy. Giving shielded units extra HP would also reward veterancy by making them slightly more resistant to power stalls.