Public vs. Private Corporate Finance/FP&A

As in private sector vs public sector? If so I would strongly advise against going into public sector. People that work in public sector are seen as uncommercial, bureaucratic and dull and in general have an extremely difficult time switching over to the private sector.

If you're talking abour private vs publicly traded companies, it doesn't matter. I've worked for tiny throught to medium sized private firms and currently work for one of the worlds biggest public companies.

Bigger companies (usually public) will often offer better career oppertunitues and exposure and can look better on your CV. That's a rule of thumb and there are obvious expections.

When picking a company to work for I'd look more at the industry they're in (does it interest you) and at how their business works. For example if you like working with large amount of quantitive data you might find it interesting to work for a large retailer / FMCG (fast moving consumer goods) as they have tons of data on everything from sales, time of day/year and weather than can be analysed. If you'd prefer to work on a more qualitive basis then perhaps a slower moving industry like construction or professional services may be of more interest.