Beastlord
Superlative utility.
Are we playing the same game?
Anyways, in regards to the original post. Im gonna assume that you simply want to be the best you can be with this duo and would reccomend you roll a cleric as one of the characters. I would also reccomend your duo be melee/healerClerics are desirable for 6 man, raids, duoing, soloing, watching youtube videos, getting loot, high fiving the pope etc etc because they are the best healer by a large margin and have pretty good mana free DPS which is nice for duoing. If cleric isnt your thing for whatever reason and you still want a healer I would roll a shaman.
Shamans are great in 6 man, great in raids, are pretty solid DPS when duoing and have pretty much unlimited mana. You cant kill things as hard as if you had a cleric, but you do smaller mobs for an extended period of time. After some EXP, shamans can do some pretty bangin DPS, to the point where at high tiers they can out DPS beastlords (Alkesh did this pre verdict).
Druids are more convenient for ports and track but both of those things you can camp one of your toons for, load a druid, port/track, then load a more useful character instead of the druid. To be honest, I find it hard to find a reason to give a druid a raid slot over a heal-mode paladin, or a 2nd shaman, or pretty much any non-beastlord class(However, when it comes to doing quest, druids are kind of helpful until you complete the quest and go back to playing better things). Almost every druid I've played with has said, "I wish I made a cleric instead", but I've never heard the reverse from a cleric, or shaman. Druids do get a kind of cool AoE nuke at endgame, but thats the only real redeeming factor that I personally see in the class.
As for the 2nd character, i'd probably roll a melee DPS class. Tanks are very difficult to gear and kind of suck without gear. If for whatever reason you are determined to play a tank though, I'd rank them SK>PAL>WAR, however they are all so close and each have their uses that I'd just play whatever one is the most appealing.
Don't roll a beastlord. I could write pages about what is wrong with that class, but if you like having worse DPS than a bard, tanking worse than a bard, having worse/less utility than a bard, have your character scale poorly with gear and experience, get made fun of by literally everyone, have your wife leave you etc etc, then roll a beastlord.
Bards are pretty good, and Bard/CLR is a strong duo. They solo pretty good as well. Bards are always wanted for literally everything, they have crazy utility and can do some pretty solid DPS as well, bottom of the real dps classes, but above beastlords/healers/tanks. They can tank okay, but are probably the squishiest of the melee classes (110% justifiable balance wise, but thematically is odd), however i mentioned them tanking better than beastlords because they have insane aggro. Bards only get turned down because people have too many of them already.
Ranger would also be a good choice with a healer, or playing solo if you get lazy and dont want to box. When they can bow, they can do top tier DPS from range while being fully mobile, they scale incredibly well with EXP/gear. They are tied with monks as the best non-WAR/PAL/SK tank class, but when they use /s 4 (Lose offhand attacks, gain parry bonus) they become the best non-WAR/PAL/SK class at tanking. In a duo they will most likely be meleeing, but from some parsing a few people have concluded that even if a ranger is in melee range they can still outparse a beastlord. Rangers are a high priority class for raid/6 man, they stack incredibly well (bringing more than 1) and benefit greatly from getting support (Bards songs, enchanter 4 tic overhaste called boon). PS they are boring as fuck unless you get a bunch of clickies and enough mana to not run oom after like 5 spells.
Monks are pretty rockin now. They do some bangin DPS with barefist and tank pretty well and are great to duo with a healer. They scale pretty well with gear until you hit the very endgame and get very few upgrades do to some wonky itemization (bw gloves cough rujik wrist cough go look at my post pls slaariel cough). In a 6 man they are cool for pulling/offtanking and provide solid DPS, in raids they do essentially the same, but less offtanking because raid mobs typically hit much harder. Im kind of biased towards monks because i play one but a lot of other people do too. Also they have a stamina bar that empowers all their special punches and kicks, its kind of like warrior stamina system but a bit different.
Rogues arent super great duo, they are relatively squishy melees and obviously do less DPS from the front which is 99% of the time when you are duoing melee/healer. However, SK/Rogue or PAL/Rogue is a pretty okay duo if the knight is super geared, but that is true for literally every class. They are one of the best DPS class at almost every point in the game if they play and gear properly. Certain very endgame fights punish them slightly due to movement mechanics, but they still do pretty well on those too. Not a lot of guilds have rogues because not many people play them, to be honest most people find them quite boring, as well as less than ideal duo partners.
Caster classes arent super effecient for duoing as they can solo pretty well and most of them excel in a Knight(Pal/SK) and Int caster duo. MAG/CLR works pretty well, so does ENC/CLR or ENC/DRU, but unless you enjoy being awful in everything but raid/6man then I would advise against rolling enchanter. I'm partially biased towards the class, but most people agree (Grinkles too!) that enchanter is the worst questing/duo class in the game, but arguably the strongest class in a raid/6man. Enchanters are also the highest DPS class in the game by a sizable margin when in a raid, and that doesnt even factor in all of their utility and damage boost they provide to everyone else.
Personally my top picks for a duo would be BRD+CLR, RNG+CLR, then BRD/RNG + SHM.
Writing this post has kind of inspired me to make a 2015 edition of Cinn's class tier thread from many years ago, maybe I will do that. I'd also advise taking some of my opinions with a grain of salt, as I'm just one nerd, but a lot of people would agree I know a thing or two about this game. This is also assuming a lot of things, like that you want to play a melee/healer duo, that class preference isn't a large factor (Realistically speaking, it is). If their is a class you really want to play then I would play that class (unless its a beastlord or druid people will make fun of you as long as you play those classes)