Why the Los Angeles Kings role is better
The biggest difference between the Islanders job and the Kings job comes down to the talent currently on the roster. While the Islanders will have four million more in cap space, they have less players under contract.
Meanwhile, the Kings have basically their core players still under contract and the biggest pending free agents are Vladislav Gavrikov and Andrei Kuzmenko. The roughly $25 million in cap space would allow the next general manager to re-sign both while also adding some top free agents to the roster.
The Kings are also much closer to a Stanley Cup than the Islanders at this point due to that fact. They have made the playoffs four straight seasons and are coming off a regular season where they tied the franchise record for points at 105. A new general manager could have the flexibility to be aggressive with some short-term moves to build out the roster for a Stanley Cup run versus a franchise rebuild that the Islanders are likely facing.
As mentioned previously, the LA Kings won't be in a position to offer both titles to the next candidate and they won't have the draft capital that the Islanders have. However, they are as a franchise in a much different position as they are trying to compete for a Stanley Cup next season, and that should be the biggest selling point for candidates.