Max was 'winning' when Natsu didn't pull out any of his stronger techs. He pulled out a single Fire Dragon's Iron Fist.
No Roar, no Wing, no Brilliant Flame, and none of his secret arts. No Crimson Lotus: Fire Dragon's Fist (the one he used to beat Gajeel), no Crimson Lotus: Exploding Flame Blade (the one he used to make Gildartz step back and to defeat Sting and Rogue).
Yes, Max was doing well when Natsu wasn't even using his best flame moves. This doesn't translate into Max being stronger than him, just that Max was doing better than expected.
Additionally, we know that emotion explicitly powers up dragon slayers, as we've seen often. He was fighting a friend who he underestimated.
I thought it required a lot of power to equip, power she wouldn't have had without the boost.
Yes, she wouldn't have been able to use that special armor without the boost.
However, if she hadn't been wounded, I'm not sure she'd have needed the special armor to at least make it close. She got some hits in before calling on second origin.
Natsu beat the guy, but he was maxed out at that point. He had nothing left. IMO, Sting would have beaten him at that current state of power.
He ran out after using Lightning Fire mode dragon's roar, which is a move he didn't use against Sting at all.
And again- Gajeel didn't have a boost like that and he was able to shrug Sting's assault just as well as Natsu did.
The way I see it, the boost let Erza use her magic-cutting armor, and it let Natsu use Lightning mode for more than one big attack. Both very important upgrades, but they have a lot aside from that.