I work at a PE-owned company (over 20 years in PE ownership now) and the strategy is to seek growth, not to cut costs by shedding headcount.

Caveats:

1. This is anecdotal evidence, and many PE firms actually do buy companies with the intention of firing people.

2. I don't know whether this is the most common activity or just generates the most press/attention. I would be pretty interested in a statistic that looks at PE company acquisitions and compares company headcount at entry and exit.