It depends on locations. Being allied can and will enhance your level of payout from minor factions.
Basically being allied (or the closer to) will allow access to more of the listed missions. It doesn't affect the presence of those missions, just whether you are eligible to take them.
It is supposed to, does not always work out though. Being tired of a mindless grind flying in haz res I figured I would take a break, do something else, jokes on me I guess.
I am currently allied with a High tech station, in a high population system, that is not at war, it was happening during a boom phase. I am also allied with the controlling faction (fed) and all I am being offered by every fed aligned faction on the station is one or two mining missions every time I refresh the mission list, (mining missions in a high tech station, they cannot even refine the minerals I am being asked to gather). Plus the odd 10k fetch and return every third or fourth refresh and once in a blue moon a mission that is actually worth doing for a pilot flying a conda with the highest rep possible.
Over two days I was able to gather up enough missions to pay out 2 million in rewards, two days wasted. It was no better in the high pop system I moved out of.
Having taken a look on the beta server, the changes there do not go nearly far enough, it is frankly pitiful more than a year after launch for such a core mechanic. I am still getting federation missions that improve imperial factions position in other systems; how the hell does that get past Q&A?
In sandbox games, mission givers are supposed to deliver bite sized pieces of structured content that make sense within the frame work of the game world. That is the basic premise behind their inclusion in any sandbox. Quick access to content that rewards standing, items, credits. If frontier cannot even get that right what hope of them sorting mechanics like powerplay or actually making faction allegiance and ranks worth a damn? They are so blinkered by the desire to add new content that they forget there is a whole lot of game already present that needs major attention.