Both have their own places and uses.
Jersey pocket, easy access but things come out unexpectedly. I use it for temporary storage for my gloves, Koolcovers etc,
Fanny pack, zippered pocket is more secure but hard to access(you have to stop the bike). I use it for my digicam, maps and wallet if I'm not wearing Sportif shorts.
And you don't have to choose one of two, you can use both at the same time by just loosening the fanny pack belt a little. If the budget is the reason you have to pick one, I would pick fanny pack.
You can get a jersey with zippered back pocket, like this
one. It's nice to have it for a wallet additionally to three open pockets. Koffee, are you listening?