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Imo it's about specialization: dungeon tanks have a lot of flexibility in terms of gear and abilities, but trial tanks need to fit with their group and eat massive amounts of damage while buffing their group in support gear and managing resources nigh on perfectly.
Ultimate: in dungeons there are lots of options, but in trials tanks are expected to use aggressive warhorn in rotation
Gear: dungeon tanks can build a bit more selfishly because of pug roulette, but someone in a trial needs to be wearing Ebon; traits matter a lot more
Damage resistance: in dungeons I usually run 27k health and 29k resist so I can use more abilities; that doesn't cut it in trials, even normal ones, where you probably want to be resist capped and have health at least 35k because the bosses hit hard
CP: you can tank a dungeon without any CP in block cost reduction, bash reduction, etc; that's not going to happen in trials
Skill: positioning and such makes dungeons smoother, but it's usually not a big deal if you miss a cue or two; positioning makes or breaks trial combat and if you're playing with any amount of latency you probably need to memorize the fights because you won't always have time to react to a cue once it appears
Communication: communication makes dungeons easier, but once the fight is explained you probably don't need it; newer trials like HoF need ongoing communication between tanks to coordinate boss switching, shield elimination, etc
And I'm sure there are more differences. \o/
CP 750+
Never enough inventory space, even with storage coffers and a mule account
Some of the newer trials, half the boss fights the two tanks are almost co-tanks. (Like HoF - the first and fourth bosses, they both do the exact same job). Aside from that, sometimes main tanking is easier, sometimes off tanking is (as far as what you manage damage and mechanics wise) - but it will require (or you may prefer) very different gear from one tank to the other. Sometimes this allows an off tank to wear more sets that will help the group more through more debuffs to boss or more shields/healing to group, etc (whatever needs might be).
Dungeon wise - well, they aren't as challenging not counting the newest dungeons usually. I actually wear my basic trial setup when I'm tanking FH or Cradle or Mazz, etc. But some of the old school 4 man dungeons, you barely need to be that tanky - sometimes I will use my Warden tank even and run a heal/tank build that also does a tiny bit of damage and we'll run it with 3 dps.
Outside of basic gear setups, sometimes players will change CP passives for a specific trial like taking all points out of physical resist and putting into magicka or vice versa because they know most of the damage in a trial will come from one source or the other. And the rest I think is just mechanics of the fight - bigger group, two healers, two tanks, longer fights and even the trash pulls in between boss fights can get hairy.
Tanking in a dungeon requires holding aggro on the boss and staying alive at bare minimum. Beyond that, you want to taunt priority adds, provide crowd control, debuff the boss, and buff the group.
In dungeons, tanks and healers are less necessary the higher the DPS gets. This is because unlike most Trials, high DPS allows a dungeon group to completely skip certain mechanics because the boss dies too fast, especially on Normal difficulty dungeons.
For Normal Difficulty: I recommend a DPS/Tank build. You DO want to hold aggro with a taunt and be able to survive - your group will appreciate you not being a fake tank. But after that, you really do want to bring some DPS. Adding your DPS to the group will let you carry a low DPS group far more effectively than being a pure tank. A pure tank can carry the group all day, but it'll take all day, whereas a DPS/Tank can carry the run quickly.
For Veteran Difficulty: Here you can get more of a pure tank/group support build, especially if you want to PUG and thus need to survive the vagaries of groupfinder or you run with an organized group that can really take advantage of your crowd control, debuffs, and buffs.