I have had two high deductible plans in the last two year (work changed providers) and here were the things I remember:
Old Insurance:
Deductible: $3,000
Tier: 2
Price: 100%/$60
New Insurance:
Deductible: $3,000
Tier: 3 (maybe 4, I can't remember)
Price: 100%/25%
It was effectively free to me on my old insurance with the copay card (covered $3600) because I would hit my deductible and then have enough to cover the co-pays after. On my new insurance it's not feasible for me to pay ~$400/mo until I hit my OOP ($6000). You might be asking why I didn't look at a PPO plan instead of high deductible, because of the drug tier there was no difference in the price.
HIV tests are still not included in routine bloodwork, even though other diseases like hepatitis are.