I was asked this question yesterday and thought it worthy of comment.
First, to clarify, "net" means after the fee is removed, while "gross" means before the fee is deducted.
There are generally two reasons we show IRR. First, in cases where the client controls the cash flows we show it to provide the client with THEIR return; that is, the return that takes into consideration not only the manager's performance but also the impact of the client's cash flow decisions. Why wouldn't we want to show "net"? This would truly reflect how they are doing, after (a) the impact of the manager's decisions, (b) the impact of their cash flow decisions, and (c) the impact of the advisory fee. So I'd say use "net."
The second occasion would be when the manager controls cash flows. As noted in yesterday's blog, I argue for IRR whenever this is the case, not just for private equity managers. Here we're showing the impact of the manager's entire range of decisions, from their management of the portfolio to their cash flow timing decisions. Net would reflect the entire impact and so this would generally be the better return, I would say. However, when the manager is providing their performance to prospects then both gross and net would be ideal. So in these cases, I'd say show both.