I don't think either is of any importance until your game is at the level where that's almost all you're lacking in, somewhere in the transition from B player to A player you should start working with at least a jump cue.
Break cue really isn't that important ever, (if you can get a good break with a normal que) then you're fine. But I see now with the new phenolic tips and the right stick they can sure crack the crap out of a rack without having to put nearly so much stroke into it that you loose cue ball control, so it does have it's value especially for those that just never had a powerful break or good cue control on the break. Women can probably benefit more than anyone from a really good break cue, since they don't have the upper body stregth to get the breaks guys do, but I'm sure most can benefit at least a little. If it's enough benefit to carry three cues and buy a new case to fit them all that's up to you. I like my case and it's only made to carry 4 shaft and two sticks.
I'm entering into A player range now after many years of play and still don't have either a jump or break cue, I can break just fine with my playing stick, but sure do wish I had a good jump cue.
Everyone I play at my level has a jump cue and they know I don't have one, so they always know I'll be kicking. That gives them a bit of an edge I think always knowing what I'm unable to do or what I will be doing for sure. I think I'd like to try one of those j&j cheapies I've heard so many good things about, but first I'm unemployed and second I'm saving for simonis coth on my own new used cheap gold crown I just bought. We all have our priorities...
You can't overlook the cost of a new case to carry all those sticks... The case I have now cost me as much as my cue and my whole used table, and I just can't see replacing it just to carry the luxury of a dedicated break cue and jump cue and playing stick. My cue is just a McDermott, I used to have a meucci originals but it was stolen. Technically the McDermott used to be my break cue and just overall backup cue, it is kind of a basic thick heavy do it all solid club really, never had the finesse the meucci did but I don't feel like I'm missing anything breaking and playing with the mcdermott. I took out the weight in the butt to play with it and it still feels like it it could probably do well clubbing down mid to large game animals if we're ever sent back into the stone ages.