All the bands I've worked in that had a bandleader have regarded that person as the leader. Making all the decisions, whilst at the same time listening to suggestions from bandmembers, but not always implementing them. They had the responsibility of getting gigs, personnel, equipment, rehearsals (very few in some bands - turn up, wear the right clothes, read what's there, get paid, go home!), and sorting out any glitches on the night. And often getting more money for it all. Why not.
On occasions, it's been my gig, and the erstwhile bandleader expects me to be the bandleader, so roles are reversed. No power struggle: everyone knows their place. There's no discussion about it, that's how it is. All my responsibility.
The decision as to how it works in your band will ultimately be yours. You are the founding member, so are the initial organiser. You could delegate tasks - trumpet leader to sort out numbers, drummer get gigs, singer has responsibility for p.a.,bassist looks after finances, and such like. Maybe an answer comes from what happens when there are problems. Are they then directed to you? If so, there's an answer. You're in charge. Be in charge!
Otherwise, run it as a corporate, where everyone has their say. Trouble with that is rather like a committee, (or a government!), it takes ages to get a concensus, and it's often a waste of time. If a player is unhappy with you as bandleader, he'll either say so or leave. So that mantle needs to be worn with a lot of experience - both in knowing the music, knowing the music scene, and knowing how to handle people. A big mantle!