It might be my personal issues with units over 260 pts that is speaking. I hate having a 300+ pts unit decimated by a single spell. In units 50+ state stroops adding shields comes at the same cost as 10 additional troops, granted that they are easier to get combat result from. On the other hand they could form a death star for your characters.
Using the above example and assuming a unit of 300 points, that equates to 50 with shields or 60 without shields.
In order to cause 60 wounds through a 6+ save, it takes 70 successful S3 wounds.
In order to cause 50 wounds through a 5+ save, it takes 67 successful S3 wounds.
Very minor difference. Almost negligible. So the arguments for and against, in this case, aren't to strong. But in light of the "extras" I mention below, I think the "extra bodies" has further advantages.
For starters:
In order to cause 60 wounds through a 6+ save, it takes 60 successful S5+ wounds.
In order to cause 50 wounds through a 5+ save, it takes 50 successful S5+ wounds.
So against S5+ attacks, having extra bodies means the unit will last longer. Extra bodies can always soak a wound, extra save is only good against low strength.
The way I think about it -- and this may not be entirely accurate, but it "feels" right -- is... If the cost of buying extra bodies is equal to or less than the cost of the armour save in order to get an average of one extra survivor from a given set of attacks, I will generally go for the extra bodies.
Beyond the mathhammer of soaking wounds, you can also potentially use the extra bodies for horde formation, and more ranks and numbers (and thus, steadfast.) The only benefits I can think of for a smaller unit is that it takes up less space and is potentially more maneuverable. I'm not sure either of those are important when you are talking about core infantry in numbers of 40+
As far as spearmen vs. halberds vs. swordsmen... I'm not going to step into that one at the moment. Personally, however, I've been using a unit of spearmen lately because, a) I have a unit of them painted up, b) I wanted more figures in my army, and c) they look cool. I may be a huge advocate of understanding mathhammer and acknowledging that it is the foundation of the game mechanics, I am no slave to the mathhammer.