Arcanine

I would think more now... it is all move matchup instead of pokemon type match up the way i see it now...

I think we will have to wait and see to see how it fits in the new overall meta, but at the very least we can talk about how it performs against its counters with the new type effectiveness rules compared to the old ones.

Previously, with SE and STAB being identical, and NVE and IMM perfectly canceling out STAB or SE, a pokemon with a NVE+STAB move had the same multiplier as a move with no multiplier. So with regard to Snarl which is fairly similar to Fire Fang, you might expect it to perform similarly or slightly better against a common Arcanine counter like a Water, Ground, or Rock mon. A move with SE damage is better than one with STAB+NVE, so in that regard Wild Charge would easily be better than Arcanine's other options against Vaporeon, but worse against a Ground type like Golem.

Now with the type effectiveness changes, the previous conclusions change a bit.

Consider Snarl vs FF against a Vaporeon or Golem. Previous multipliers:

Snarl: 1x
FF: 1.25*0.8 = 1x

New multipliers:
Snarl: 1x
FF: 1.2*0.714 = 0.8568x

So given that FF is ever so slightly worse than Snarl based on attack power, Snarl easily is the better quick move on defense.

For the charge move, it's not quite as clear cut, because you have two things to consider: Are you being attacked by a water type, or are you being attacked by a Ground type?

If water, the multipliers are:
WC: 1.4x
Crunch: 1x
FB: 1.2*0.714 = 0.8568x

All things considered equal, the WC multiplier is obviously better. It then comes down to comparing the moves energy consumption, animation time, and base power, and I think in this case WC is the clear winner.

Now consider a Rock/Ground attacker (Golem, Rhydon)
WC: 0.51x
Crunch: 1x
FB: 1.2*0.714 = 0.8568x

Here, Crunch has the best multiplier, while WC is the worst. Considering the moves, I don't know how WC vs FB would compare - it may be that WC is still better due to firing more often, but I doubt it. However, Crunch is the clear winner in this case.

So comparing Arcanine to common defenders, you want Snarl for the fast move, and for the charge either WC or Crunch. Crunch is the safer bet as it will work fairly well against most attackers, while WC has some incredibly good matchups against water types, but horrible matchup against a Ground type which has the immunity multiplier. I guess it comes down to preference.

Now, as to how Arcanine fits on the defender stage in the new meta, it probably isn't close to top tier, but it certainly does better against its common counters than it did before the type effectiveness changes.

It's annoying to fight, decent stats and no double weakness. Stick it in gyms that have counters against Rock/Ground.

I have a 96% Snarl/Wild Charge Arcanine I may just max out. Think at my level the CP would be around 2724. They hit pretty hard and Wild Charge can deal with the tons of Vapes that would be attacking.

I have another 96% 2723CP FF/FT Arcanine that I use for attacking but also put in gyms and he can be pretty beastly.

Wild Charge is stronger against water now, but much weaker against ground.