Are we talking about Parallax/Hal Jordan/Spectre?
Parallax/Hal Jordan?
Or Parallax the parasite by itself?
As both Parallax is basically an cosmic entity that fears on fear... I doubt it could be destroyed... and if Darkseid is truly inherently required by the source as so many others (not myself) state... than it would end up being a stalemate
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"in some cases because the writer knows that Character A will dominate Character B easily and refuses to allow this to happen for the sake of the story."
Darkseid when well written (that is, not Jobberseid) is a veritable juggernaut of power. No matter how you look at the dude he is basically soaked through-n-through with kick-ya-arse abilities.
On top of that big-D is basically the DC version of a certain Mad Titan (actually I believe Thanos was inspired by big-D), and as originally written (although every now and then writers forget this) big-D is a genius, extremely resourceful, capably ruthless, and can use the Omega Effect for everything ranging from scattering sub-atomic detrus to cooking a fab omelette!
Then there is that whole connection to the Source.
However he is up against Parallax. Basically your garden variety universe destroying reality warping I-can-do-anything-I-like unstoppable force!
I'd say Darkseid, as powerful as he may be, is simply out of his league here.
Parallax takes this.
Caveat: Let big-D have the anti-life equation and the match gets a tad bit interesting. That would be the equivalent of Thanos with the IG or HOTU, and thus it would be quite a match.
Off-Tangent: And according to one DC one-shot (which was more of a joke, but did have some interesting aspects in it) the anti-life equation is actually 'Batmite + Mr Mxylpztk (sp).' And in that one shot they went on a multi-verse destruction rampage where they were wrapping up universes like shredded paper, and they even came to our own universe (written to say they came to our reality). Hence using that benchmark (that the ALE is batmite+MrMxy, which is a stretch since that whole comic was largely very well written humor, but humor all the same) then it is apparent that the ALE would pack FAR more punch potential than Parallax could dream of.
And at the end of their rampage the two imps simply wished everything back to how it was before.
Anyways, PArallax wins. However give Darkseid the ALE and all bets are of, and the odds flip over to Darkseid's favor.
Also when Joker had attained Mxy's powers in Emperor Joker, Darkseid came into the story at one point, and had stated that Joker achieved the anti-life equation.
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When? If your referring to the recent Sinestro corps arc thats hardly the case. Hal was getting his ass kicked and didn't defeat Parralax as much as he aided in releasing Kyle from Parallax control. In fact, Parralax consumed Hal as well before losing control of Kyle thus being defeated. He wasn't defeated in a combative sense.
Either way, Hal would likely defeat DS on his own.