While they are assholes, and I may not agree with all their ideology, I think the Brotherhood has the resources to actually help the wasteland. They actually get out there and run patrols, and fight the raiders and super mutants. The reason they horde all the tech is to prevent humanity from destroying itself (again).…

The Minutemen, mostly because they’re honest and only looking to help. They don’t ask you to go wipe a bunch of people because they might be a threat. They aren’t single minded on one purpose and they don’t want to kill everyone that is different. Also choosing them allows you to not go and murder another faction.