Reed will humbly recognize that Adelaide is a better fit for the colony and step aside. If you kill him, you have to kill his guards too. And you risk losing Parvati as a companion if you don't have 10 Determination to convince her that murdering her boss in cold blood in front of her isn't that big a deal.

Should I side with Edgewater or the deserters?

If you decide to redirect the power to Edgewater, you'll recieve 2,828 XP. Your reputation with Spacer's Choice will increase, while your reputation with the Deserters will increase. If you're planning on unlocking the trophy to 'Permanently Save Edgewater,' then you must redirect the power to Edgewater.

Should I let Adelaide take over Edgewater?

This presents two options: you can go back to the Saltuna Cannery and kill Reed Tobson, or if you have high enough stats, you can actually convince him to step down from his post and let Adelaide take his job. The decision is ultimately yours to make, as there's no special reward for either option.