Depends pretty highly. Associates do well for being in NYC. VPs are comfortable. After that depends pretty highly on group or fund, but no one above a VP is struggling in any sense of the word
Just google search the heidrick and struggles private equity compensation report. The funds you name are in the largest fund bucket. Entry level, called associates, make about $300k/year. Early tenure partners (10 yoe) are about $1.5m/year cash, with about $30-40m in stock (carried interest) which can be divided by 5 years to arrive at a notional per year equity award.
At what level? Analysts are paid lower than engineers at FNG while putting in near-banking hours, whereas the top 5% who survive the climb to exec/partner-level by making it rain for the firm can rake in fair carry
I'd say associates are anywhere between 200-350k all in. VPs 300-500k. After that I have no information
My sense is 200-400 for associates and 300-700 for VPs.