TL;DR at the Bottom!!!
As you know, NUWW has been significantly changed, targeting high-damage carries like Gunter and FP (and the occassional Rattleballs :P). Now there is much more risk with less utlility in building full damage. Now, since you need to build armor/shields for CDR NUWW better fits PD characters that have a bit tankier role, like Ice King, Lich, and even Jake. In this analysis, I want to compare the nerfed NUWW Gunter with the Fridjitsu AD Machine Gun-ter.
Nearly Ultimate Wizard Wear Gunter
Last patch, NUWW (4/4/0/0/2) was easily stronger than AD. The only thing you'd miss out on was 350 attack speed, 10% more CDR, some speed and crit for a whopping amount of PD that makes your abilites one-shot the enemies. Now, at Lv 10, here are the stats for the new NUWW (4/4/0/0/2).
Attack Speed: 750
Armor Breach: 10
Shield Breach: 0
Crit Chance: 1
A. Vamp: 0
P. Vamp: 15
H. Regen: 12
The real difference in this build is the attack range debuff from the Eyeball Whip. You go from 5 to 3.25. To put that in perspective, your attack range is almost as small as Jake's W! This makes basic attack poke nearly irrelevant, because you're far too squishy with 650 health. You also lose the 10% CDR you used to get, only being able to throw out your main damage source (Wing It) every 5 secs.
Although it has its downsides, you can't forget that you're still the ultimate wizard. Q and W combo alone does 463 damage, usually enough to one shot people from half health. You have great burst and poke potential but are very vulnerable when your cooldowns are down. You also have your ult for teamfights, dealing 453 damage for 6 seconds, dealing 2713 damage total (not including shields. nothing is including shields right now). Of course, the downsideis that you're completely immoble for the duration, and people can walk/dash of your ult so they don't take all that damage. In the end, you have a 182 damage every 9 secs (20 dps from your Q), 281 damage from your bottle every 5 secs (56 dps from your W), and 2713 every 42 secs (64.5 dps from ur ult). With an average of 140 dps (without basic attacks), you're very weak in an extended fight, but If you get the full duration of your ult off and hit all your abilities, that can be a terrifying 3176 dmg after about 7 secs.
Summary: AP Gunter has much poke and burst potential, relying on his long range abilities to do damage, assuming you play from a safe distance. You have a strong mid game damage and assassination potential and strong teamfight and poke late game. However, with your cooldowns down, you are a sitting duck, so the shorter your fight is, the better.
Attack Damage Fridjitsu Gunter
Let me just list down the instant downfalls of AD Gunter with Fridjitsu (4/2/0/0/4). You are susceptible to CC, you have to play a bit closer to the enemy team, and are slightly weak early game and extremely weak mid game. The good sides is that you get more utility from The Art of Fridjitsu and are a TERRIFYING late game monster if you're not focused right away. You have very strong splitpushing with your attack speed and passive and can take down towers in a matter of seconds.
I won't do as much calculations as I did in the NUWW Gunter because abilities aren't as important, but here are the stats:
Attack Speed: 400
Armor Breach: 10
Shield Breach: 0
Crit Chance: 36
A. Vamp: 0
P. Vamp: 5
H. Regen: 12
Let's calculate the main damage source: your basic attacks. You can throw out 2.5 basic attacks a second and with 140 damage + 10 Armor Breach, you do an average of 450 damage per second, every second. Your dash is on a 7 second cooldown and does 88 damage, but shouldn't be used for damage. It's better to save it as utility, such as gap-closing or getting away. Your W does 116.5 damage every 4 secs, and should be used right after a basic attack, in is your main damage source early game. You'd be better off throwing a basic attack than a bottle late game if you can get in range. His ult does 106.5 damage for 6 seconds with a cooldown of 34, for a total of 639 damage. You should use it freely to clear waves or jungle camps, because in teamfights, you're much better off chucking basic attacks like a maniac.
Excluding your abilities, you do 450 damage per second without any cooldown, so you can hide in a bush and basic attack them to death before they can even attack. You have a lot of damage potential in teamfights but are forced to stay in the back, due to your extreme squishiness and vulnerability when locked down. Your strength is in late game split pushing, but you can probably get one-shot by the AP Gunter unless you dash away. Then again, if you can surprise him if you can burst him, you'll kill him in seconds.
Gunter is the Nidalee of Battle Party. Before, he would one shot his enemies with a long-range skillshot and finishing up by jumping on them. Now, after the changes, he can take on the role of auto-attacking/split-pushing threat that can be just as strong as his AP counterpart after its nerf.
Conclusion: AP Gunter is a strong poker throughout the entire game with big impact on teamfights with his ult. He can also quickly assassinate others with your full combo.
AD Gunter is a split-pushing, 1v1 based champion who can get quickly assassinated. However, if he can use his dash smart enough to survive, he can pour out more damage than AP Gunter in a sustained fight and take down towers in seconds.
Thanks for reading my thoughts on Gunter! Hopefully you can try both and see which style of play you like better.