How it works out depends on many of the other factors that go along with it, as other answers have mentioned. This post: http://mythcreants.com/blog/creating-matriarchies/ goes into some of these factors.
Risk and adventuring
But one crucial area is how they would view risk and property. Females would likely be much more risk averse because they have much more on the line. And they will get even more risk adverse with age. Males have comparatively less to risk.
In addition to having less at stake (fewer potential years to lose) they also have a greater time pressure. A female could take a decade to compose a poem and think little of it, if a male is to make his mark, he must do it while young.
So, barring some other factor to change it, I would expect that nearly all adventuring in the traditional fantasy sense would be done either by males or young females. Without some strong impetus, I would expect extremely few older females to adventure.
On the other hand, the females would probably hold most of the property. Simple compound interest works heavily in their favor. They'll also just be around longer to accumulate more. Even if somehow the bulk of the income were earned by males as a group, it would wind up in the hands of the females over time.
Which brings us to inheritance. The system of inheritance they use will matter a lot. If wives inherit from husbands, especially if they inherit substantially all of the husbands property then that handing over of the money to the female side will happen fast. On the other hand, if the system is more akin to primogentra (where the first born son gains virtually everything the father had). Over time, I still suspect most of the money would wind up with the females for several reasons, but it means that at least the first born sons would be a bit less eager to rush off adventuring.
And finally you wouldn't expect a lot of males in professions that demand decades to master. Conversely, while a female might do well in a simpler profession, it would be a poor decision on her part to go into one. So, in traditional fantasy terms, you would expect most wizards, clerics, and skilled craftsman to be females. You would expect most fighters, rogues, and laborers to be male.
The other factors matters.
Of course while I think that is what is most likely to happen, that can all be drowned out by the other cultural and physical patterns. Its not at all hard to imagine a culture of dryads with the females living much longer where that very reason reinforces a patriarchy.
Imagine the males, driven by the need to make their mark now, do exactly that. They go adventuring, and in absence of external threats, they go to war with each other for power, wealth, glory, and to prove they can. They get their power and walth, or at least the successful ones do. They seize power by force and begin to view the females as property. Long lived property to be considered accross generations, but then the same is true of land now, and a female in this society is bound to a tree and thus bound to the land.
When a powerful man dies, his son will claim all that belonged to his father as birthright, including his own mother. (Unless of course he is defeated by another male that takes it all by force) Now of course a long lived widow like that can't just be declared a widowed mother to be doted on. But she can certainly be traded for some other man's mother and passed around through the generations.
With centuries more experience then the men, it might seem like the females could easily amass the power and wealth over the years to overthrow the men. But their very longevity makes them too conservative. Instead, they don't do anything that could put them at risk, including angering a violent, hot tempered male. So instead, trapped by the desire to continue their long lives and protect their long lived daughters, they meekly submit to an ever changing roster of aggressive males.