Consulting vs. COS at Startup

Coming out of grad school, debating two options. Background is in data analytics and pivoting to healthcare. 

Option 1: Big 4 / Tier 2 Consulting (Think Deloitte / Accenture)

• Role: Healthcare Strategy Consultant (Associate / Senior Analyst level)
• Pros: Structured training, solid brand name on the resume, clear promotion timeline. Work would be focused on provider/payer strategy and operations. TC is $170k. 
• Cons: Worried about getting staffed on massive IT implementation or system integration work rather than pure strategy. Comp is standard for this tier.

Option 2: Chief of Staff to C-Suite at a Top-3 Non-Profit Healthcare System

• Role: Chief of Staff (supporting CEO)
• Pros: Incredible high-level exposure, sitting in on board meetings, high-level operational strategy, and direct visibility into the exact industry I want to build a career in. Massive responsibility early on.
• Cons: Less structured training than consulting. Name only recognized in this niche part of healthcare. TC is $145k but clear path to more comp. 

My Goals: Long-term, my target is to stay within healthcare, specifically corporate strategy at a major health-tech firm, healthcare venture capital/growth equity. Could see working at this startup long-term. 

Given that my end goal is to stay in this specific sector, does the structured brand name of a major consulting firm still carry more weight early on? Or does the insane, direct C-suite exposure at a massive industry player jumpstart that path faster?

Appreciate any brutally honest feedback on how to weigh these.