Not a TL:DR
Tanking:
Both classes are more than capable of tanking up to M+15, but Brewmaster will eventually become the best tank out of the two, and is always the number one option for progression raiding. If you’re looking for a more laid back tanking style, Guardian is going to be the best choice. Brewmaster can be hectic at times, and requires more micro management.
When playing solo, Guardian is going to get you further than Brewmaster.
DPS:
Feral has the potential to do more raid dps than Windwalker, but Feral is far and above the most punishing spec in the game to play poorly. In PvP, Feral’s offhealing, stealth, and abundant crowd control make it a great open world pvp spec, and is somewhat successful in 2v2 and 3v3. Druid also has the ability to teleport out of world pvp with a 1.5 second cast time. It’s a toy that will teleport you to a “natural” location. This is basically bubble-hearth. Stun the enemy, cast it, you’re gone. You can end up almost anywhere in WoW though… sometimes it’s better to just die.
Windwalker on the other hand, has a pretty straight forward rotation. It has clear choices, and the average person will do more dps on WW than on Feral. WW in arena is one of the top melee specs. You have multiple tools for crowd control, anti-healing, and the highest mobility indoors. WW Monk has roughly double the representation at 2k over Feral, but this may also be due to the number of people playing each spec.
Ranged:
Druid has it, Monk doesn’t. Moonkin is, and always will be, one of the strongest specs in the game. If you don’t enjoy Moonkin, this isn’t an issue.
Healing:
Both Druid and Monk have extremely strong healing specs. Mistweaver being the strongest single target healer in raids, and Resto being, by far, the best M+ healer. Both of these specs have multiple options for utility, and healing multiple targets at once. They also both have a “weaving” dps rotation, “kittyweave” vs “fistweave”. These more advanced rotations allow for a Druid to weave moonfire, rake, and rip in between their healing HoTs to provide a boost in damage to their group. This is the main reason Resto Druid represents roughly half of all high tier M+ dungeons in WoW. While Monks do have this option as well via Fistweaving, their dps is not as strong, and depending on the group you’re playing with, can be frustrating. Fistweaving Monks also don’t have the healing throughput of Resto due to the nature of HoTs and almost 100% uptime.
Transmog (the most important part):
Windwalker Monks’ weapons disappear when using jab, it’s annoying, so if I were you I would suggest the moment you are capable of buying them, buy the training “gloves” which are actually weapons you transmog, which make your weapons disappear so you can actually use your fists. The other specs don’t have this issue, and there are some amazing transmog sets for Monks.
As a Druid, unless you’re a Moonkin using Glyph of the Stars, or Resto, you aren’t going to see your transmog, outside of special Legion animial forms or the fire kitty toy.
Farming: Both Druid and Monk have teleports, which allows for old world dungeon farming. Druid also has the ability to teleport to a random “natural” location, which can be used to quickly get to different zones. Moonkin is the ultimate open world farmer, no other class / spec can pull as many mobs and kill them all without dying.
Did I miss anything? I’m typing this in a Heroic, so sorry for the formatting lol. When you’re overly geared as Mistweaver, all you need to do is spam 1 button every 6 seconds for AoE healing. Druid needs 2 buttons xD