Which is your best dodging attacker?
Or which "feels" like it's your best one? Out of all the high level Pokémon I own, I 100% prefer the variants that have the better dodging-enabling movesets. My second Espeon came out with Zen Headbutt and it feels much better to handle than my Confusion one, so I always prefer to lead in with that one. Also, I was lucky enough to get a (crappy IV) DB/DC Dragonite before it became legacy and I prefer to use it over my perfect Dragonite with DT/OU (I hate using that yellow Barney) , regardless of the supposed higher DPS. In my opinion, it feels safer to use Pokémon with movesets that let them dodge within a more precise window of opportuinty and frequency when battling as it also lets me push out more charged moves before the Pokémon faints, even during raids. And now that Niantic has reduced the amount of potions and revives acquired through pokestops, it seems like this will become a more pressing issue for many players. DPS alone won't determine the effectiveness of movesets anymore, at least until Niantic decides to switch back the items rewarded from spinning.
My very favorite Pokémon to dodge with is my FS/OH Moltres. If you've ever used one with that moveset in battle, you've probably noticed that it can dodge almost every attack even if you're spamming your screen like a maniac. It registers dodges like no other moveset on any of my other Pokémon, so swiftly that it feels like cheating. For that reason, I prefer using my Moltres over any of my Machamps against a Blissey.
Answers
I used to dodge everything, but I got out of the habit when the dodge glitch appeared and made dodging a liability instead of a benefit. Now I usually just try to dodge charge attacks in most battles, and frequently don't even bother with that, if it's a normal gym fight against something not at full motivation. I do still prefer to use moves that make it easier, though, like my Mewtwo has Psycho Cut instead of Confusion, so I dodge quite a bit with him. I also powered up two Exeggutors with Zen Headbutt instead of any with Confusion, back when they were my main attackers for almost every fight. I could almost always squeeze in two Zen Headbutts between every attack, then dodge successfully with a single swipe. And now, I do really like the Thunder Shock/Wild Charge combo on my Raikou, for dodging ease. Sometimes I use him as a generalist for that reason.
I sure wish I'd been using more attackers with easier dodging yesterday, though, during a Suicune raid. With three of my four best attackers, the Suicune kept using Hydro Pump in the middle of my charge attacks (Solar Beam and Zap Cannon) so I only managed to use one successful charge attack for each of them (although the one time I did manage to dodge, it glitched me). Then the fight ended at such a close margin, we actually beat it, and THEN it told us time was up. If I'd been using a multi-bar attack with any of those attackers, I bet it would have made enough difference that our win would have counted.
With the abundance of water types in the gym meta my new favorite has become by Raikou with Thundershock/Wild Charge. Every other attacker is a distant second for me. He's super fun to attack with and does lots of damage. Always have to be careful with a Gary or Vape with Hyrdo Pump, so I like my Raikou for this reason. He's been my go-to electric attacker ever since the first day Raikou dropped here in North America at the beginning of September.