Incoming SA in public finance - potential exits?

Good question, both Infra and HC are good choices. Those were my top choices when I joined the industry originally. I picked the Infra route do to politics / leanness of my team originally. Since then, I've had the chance to lateral to the NFP HC team at my BB and at another BB, but passed (I'm biased I guess). 

Now for someone new joining the industry it depends on the exact bank. In general I'd say the following (Banks in Alphabetical Order):

• Bank of America - Infra=HC (I would note the Corporate Guys (i.e. Waste Management) are in LA. The Transpo team does the Transpo P3s (I.e. NTO). BofA hired the Airport P3 MD from Citi and they are especially strong in that specific space). The HC team does well with financings, but isn't a major advisory player. If the Corporate and Transpo P3 teams were together then I'd say Infra>HC)
• Barclays - Infra>HC (Strong in P3 Transpo historically and recently hired the bulk of the Citi Infra team, who cover a mix of Transpo and Renewables. My guess is this will be the best Infra team on the street (Citi was the best before the exit across 3 of the 4 verticals). They probably do the most advisory work on the street. The HC team at Barclays isn't super strong.)
• GS - Infra=HC (GS has the best HC advisory team in the industry by far (they are weak at financings though). The Infra guys there are strong in sports (one of the co-heads of their sports team is from PSI) although they focus that group on EU deals. Their main Infra MD away from sports recently went to RBC. If you are interested in Sports at all then Infra>HC)
• Jefferies - Infra<HC (Hired bulk of Citi's HC team who are probably 2nd in advisory and still strong in financings. The Infra guys are competitive, but are much smaller than most of the street. As a bank and a department they've had a ton of momentum, but culture is incredibly tough for PubFin. The Infra team does renewables and social infra, while transpo handles P3s.)
• JPM - Infra<HC (JPM has the best HC financing team on the street full-stop. They don't do a ton of advisory though. Their staffing model is odd/unique, but they remain strong in the Infra space across the board.)
• MS - Infra=HC (Both groups are strong in general, with the co-heads of banking coming from the Infra and HC teams respectively. The department has had a ton of turnover in general at the senior level, so it is tough to give more guidance. They did hire a senior banker from Citi to focus on Social Infra, so they will be strong there)
• RBC - Infra=HC (The Infra Seniors are strong in social infra and are competitive in Transpo P3s. The HC team is strong and financings and advisory. I might lean HC, but its close)

If you focus on the Infra / HC industries specifically, I'd say the following is true (post Citi's exit):

Infra/Project Finance/P3

• Transportation - 1/2) Barclays=BofA 3) JPM 4) RBC 5) Jefferies 6/7) GS=MS
• Renewables - 1) Barclays 2) Jefferies 3) MS 4) Everyone Else
• Corporates - 1) BofA 2) JPM 3/4) MS=Barclays 5) Everyone Else
• Housing (Social) - 1/2) MS=RBC 3) Jefferies 4) Everyone Else
• Stadiums (Social) - 1) GS 2) Everyone Else

NFP HC

• Advisory - 1) GS 2) Jefferies 3) RBC 4) Everyone Else
• Financing - 1) JPM 2/3) RBC=MS 4/5) Jefferies=BofA 6) Barclays 7) GS