I am strongly in favor of halberds over spears, and I'll try and supply some of my personal mathhammer.
As I see it, halberds can do everything spears can do at least 80% as well. And there are some things that halberds can do 300% better. So halberds are the most robust, all-around, fail-safe, all-purpose, all-comers, etc. The stuff that spears are better against are the stuff that doesn't matter because you'll win anyways (fighting gnoblars or skinks or having mindrazor), while halberds help in the fights that are life or death for your line/army. I'll also focus on the attacking, because I likely would never give shields to my spears, and against the opponents I consider it wouldn't matter. No parry saves for the spearmen.
1a) Horde of Spearmen vs. Horde of Chaos Warrior (hand weapon, shield)
Spears kill 1.8 warriors (40 attacks, 50% to hit, 33% to wound, 33% get through armor, 83% not parried)
1b) Horde of Halberds vs. Horde of Chaos Warrior (hand weapon, shield)
Halberds kill 3.1 warriors (30 attacks, 50% to hit, 50% to wound, 50% get through armor, 83% not parried)
2a) Horde of Spearmen vs. (T6!!) Doomwheel
Spears do 1.1 wounds (20 attacks, 50% to hit, 16% to wound, 66% get through armor)
2b) Horde of Halberds vs. Doomwheel
Halberds do 1.0 wounds (15 attacks, 50% to hit, 16% to wound, 83% get through armor)
3a) Horde of Spearmen vs. Mournfang with Wyssans Wildform
Spears do 0.4 wounds (40 attacks, 50% to hit, 16% to wound, 16% get through armor, 83% not parried)
3b) Horde of Halberds vs. Mournfang with Wyssans Wildform
Halberds do 1.8 wounds (30 attacks, 50% to hit, 33% to wound, 33% get through armor, 83% not parried)
I grant that these are situations which strongly favor the Halberds. However, these are the situations which often are very important and also very likely to occur in practice. They certainly did in some recent battle reports. And I can't conceive of a situation where a spearmen is twice as effective as a halberdier, but as you can see the reverse is very common. And then we have the current shift of the metagame is towards monstrous cavalry, knights, etc.; which is definite halberds territory. Spears also have additional strategic drawbacks. They don't get extra ranks when they charge, when they're hit in the flanks, or when they've suffered losses due to attrition (which I ignore in my analysis, assuming conditions are ideal for them).