@~Charging Lightning~ sorry if it looked like I didn't pay attention to your points, I did, it's just that your points are mainly a matter of opinion.
Your points were:
1. Ikatsunagi has shown pain before, for example, when Natsu finished him off.
My opinion: He may be showing pain or his open mouth may be an indication his face has been torn apart in pieces so his jaw was no longer joined.
2. Jacob blocked the kick, so of course he isn't going to be as damaged as when he took Natsu's punch to the gut.
My opinion: so you're mixing real durability and passive durability. If an attack takes you by surprise it's rather clear it's going to affect you more than it should. For example, it's likely that August could block most/all of Erza's attacks, but then again he got pierced by Brandish, who does not specialize in cqc (which leads me to think her strength is inferior to Erza's). So yeah, of course you've got a point but I don't see that punch in his belly and his expression of pain as an indicator that his durability is low or anything.
2.5 The point is that he was still affected despite him recovering quickly.
It's hard to account for things like that. I mean Wahl was literally destroyed by one attack from Laxus, Erza was hurting Ajeel... They're not made of diamond that's for sure (although we don't know if Natsu's attacks could destroy diamonds, maybe they could...), but what I mean... sometimes it comes down to opinion. A face of 'pain' can indicate than an attack actually hurt a lot or that he just got surprised by the fact it hit... you get my point?
3. That Natsu's punch against Ikusatsunagi had prep/charging up, so it must necessarily make it more powerful than the one against Jacob.
My opinion (and probably the truth, thanks to calcs): Although as I said in my previous post, "since we don't know Ikusatsunagi's durability, it's hard to say 'how hard it is' to tear him apart, as in how many megatons it takes", the truth is that Natsu entered a mode whose aura allowed him to literally evaporate a lake, which is a mountain busting feat. So my assumption and personal opinion is that a similar punch in a more powerful mode is necessarily going to make more damage than the same punch in base, even if that punch in base had charging up, or even if emotions played a role.
People tend to try to reason out/account for the feelings/emotions of a character in a certain point by means of his face or how many veins are shown or how frowned a character is, when in reality
it is an indicator, but people convey their feelings in different ways in certain occasions. So you may claim Natsu was very pissed off when fighting Ikusa therefore he was more powerful, but Jacob was about to kill the entire guild and Lucy, and severely injured Mavis, so he must've been angry as hell too.
My overall opinion then is that indeed, emotions play a role, charging up an attack plays a role, but what plays the major role is that a superior mode is always going to outclass a previous mode. An uncharged FDKM punch is likely gonna be stronger than a charged up base punch. I'm not taking emotions into account here because whenever Natsu activates FDKM, he's probably bloodlusted.
Your opinion is that if Natsu had used his true strength against Jacob, he'd be pushing up daisies. I respect it.
On a side note, I generally don't believe in calcs, especially size calcs (to calculate the size of, say, Fiore vs shrunk Fiore), I think we try to think more than the author does when the author probably does not pay too much attention to the scale of a given attack because in his mind, x attack is superior to y. But I think calcs sometimes help give us an approximation to the author's thoughts. In this case I think it was the author intention for us to understand that the punch Natsu used against Jacob was much superior than the one he had used against Ikusatsunagi, especially due to the fact he was using a mode whose mere presence was evaporating a lake. But, again, it's hard to get exact numbers from something we don't have too much data. Only Hiro knows many questions that we try to reason out by means of calcs or logic/opinions.