Gun Fu is not situational at all, you can fight almost all fights with Gun Fu. The playstyle here is that you run around with Hit&Run and kill everyone in 2 turns (first turn ending in Stasis) from melee range. There are some exceptions (eg, when the enemies are coming in waves, like when the Natives are attacking the camp), but very few.
As I said, you can run up to most/all enemies with hit&run, but at point you're paying 2 feats and 7 AGI for a moderate skill increase, possibly even not hiding behind corners to break LoS. It's a big investment and pretty low priority given how many feats pistols can take.
Gun Nut is not great, but it is OK. One point in PER will give you 4% more damage and 2% more precision (so let's translate this to roughly 6% more damage), Gun Nut gives 7.5% (EDIT: It is more than that, see Mandriller's post below. ). It is an acceptable bonus if one already has INT6 or 7.
I did some tasting, Gun Nut on a +/- 160 quality .44 hammerer will improve damage from 26-122 to 26-141. That's about 13% increase in average damage, not terrible. 1 point of PER is as you said around 4-5% increase in damage, precision is bit more tricky to quantify. I suppose for Vers build that already maxed DEX this is an alright way to increase damage, but again, so much better stuff to take before a moderate damage increase. You're still about as likely to roll really low and do nothing though, only slightly less.
Point Shot and Kneecap Shot don't make much difference for Versatility builds. I have more than 20 shots/turn with a 9mm. Point Shot will give me one more shot, ie ~5% increase in damage. Less than what Gun Nut gives me.
Point shot is not a must have for firearm pistols that's true, but with smart bonuses it will deal around twice the damage of a normal shot. Kneecap on the other hand is invalueable just for reducing enemy MP to 0. It's yet another way to disable melee enemies that will also work if they're immune or resistant to stun/incap/immobilization. The damage is pretty great too, with smart bonuses initial shot will deal about twice the damage so the bleeding wound will deal around 250% of normal shot damage. So all in all, if you let the thing live long enough to take all bleeding damage (reasonable vs. bosses), it's the equivalent of shooting 4,5 times.
Belts:
105 AP/turn with 4AP/shot for my 9mm. 1 reload per turn drops my available AP to 101 AP or 90 AP depending on belt. That's 24 shots with bullet strap belt (EDIT: can't go more than 24/turn due to magazine capacity) and 22 shots with commando, so that's a difference of ~10%.
According to my calculations, the Commando belt gives 10% damage and 5% precision to Versatility builds. Someone might want to recheck this because I did the calculation in my head one night that we had electricity outage, but I think it is correct. Therefore, it gives me what it takes away and more, assuming the build has been designed properly.
Man if you're going 9mm then Vers becomes even less attractive. All you need to reach 4 AP/shot with a rapid 9mm is 17 DEX. Base AP cost is 20, 17 DEX reduces this to 12, gunslinger to 9, 50% decrease from specced bullet time rounds down to 4. You could honestly go with only 15 DEX and use SSD for the fights that would justify needing 4 AP shots. If you're going to have SI all the time and die from a sneeze, you might as well go with 12 DEX and reach 17 with All-In+SSD. At that point a Vers build is going to have very low skill.
Now let's take a look at what happens when you can go for 11 PER and have 10 spec points to spend on something that isn't vers. Your skill is going to be slightly worse than 18 DEX vers with commando belt, but not too far off with juice+marsh honey and you do get a few shots more per turn. You're probably a few % of damage behind.
On the other hand you can pick up sharpshooter and max crit power spec for example. Vers build with crit power and hammerer is going to have only 150% crit damage bonus. 11 PER build is with sharpshooter and 10/10 crit power is going to have 265%. In total damage terms that's 250% vs. 365%. About 50% total damage increase and you should be critting nearly if not all the time with the 11 PER feat that increases crit chance by 7%, SI and/or Ambush (that also requires PER and boosts hit chance a lot by cutting evasion). Keep the measly, unreliable 13% increase from Gun Nut and similiar, conditional increase from Gun-Fu, this is much better. You have more shots, each is dealing more damage and you also get nice stuff like kneecap on top.
It's really not that clear which is better honestly, there is a lot going on in both.