Yes, most venture capital (VC) and private equity (PE) investors need to rais money themselves, usually from institutional investors (large insurance companies and asset managers).
When pitching, these investors often make the same mistakes the companies pitching to them make. The most common one: a story that is not very differentiated. Careful deal selection, deep involvement with your portfolio companies, really working with management. Institutional investors get pitched all the time by VC/PE funds that say exactly the same thing.
The best VC/PE investor pitches are those that tell a story about a really distinctive type of investor, where everything reinforces each other: the backgrounds of the investment team, the deals you picked, the exit track record. Some funds have great access to deal flow in the telecom industry, some funds are really good in bidding for privatizations, some are really good in turnarounds, some have a really deep understanding of bio molecular structures, some have a unique skill in stitching together innovative financing structures. It is very rare that all of the above work for one fund.