Overall, it's been great having a companion to tag alongside my chars while I'm rustling around in PvE overworld stuff (though having to redo the quests on each char -- when you have 2 full accounts [(18chars x2accounts) x 2companionsperchar = an obscene buttload of repetition] -- gets quite tedious.
Since messing around with them, there have been a couple things that I would reeeaaaallly love to see with respect to the companions. These are simply my own thoughts on the matter, and while I may speak in generalizations, I am in no way trying to speak for the whole ESO community. I am, however, hoping that there may be others who also desire to see these changes, and as such, see the ideas gain enough gravity to become implemented into the game.
1) Individual outfits.
Only being able to choose a single equipment motif for the outfit of each companion that will be displayed across all of your chars really reduces the fun for me. It severely reduces the customization of the companions for each of the characters I have. I think it's great that the companion progression in terms of skill lines and level is account-wide: this was a great idea! However, certain aspects, in my opinion, should be character-based. One of those is the ability to have a unique outfit for each companion on each character. I recognize that you can use costumes on each one, but many of us have spent a lot -- like a LOT -- of gold on the motifs that we like. It would be truly awesome to be able to match our companions individually with our characters in terms of their looks.
2) Individual skill bars.
One of the things I was most excited about in my anticipation of the companions was the ability to customize them to accent each of my chars. Some tanks don't need any extra heals, but would be great with more dps. Some dps can also self-heal well, but would be accented more with a tanky-dps hybrid, while others don't need any dps help, but could use a healer with some tankiness, etc. There's lots of different pairings that can go with lots of different playstyles. Instead, it's a "one-bar-fits-all" approach for each companion. Granted, there are two, and of course we are anticipating more in the future, which will help with this particular issue a bit. However, given that each companion has their own likes/dislikes and personality for your char to mesh with, Bastion/Mirri don't always fit with a particular character; having to share the skill bar account-wide is a further limitation then. As I've been going through getting the companions on all my characters, I've seen that I need to kind of settle on a role that'd be used account-wide for each comp. For my own uses, I've set Bastion as kind of a DPS with some tank-y aspects, and Mirri as a healer (with a splash of DPS thrown in). As an example of a clash, my nightblade healer is a bit of a criminal (dark brotherhood/thieves guild); normally I would pair her with Bastion to fill out her strengths, but as he is a prude about crime, I am somewhat forced over to Mirri instead, except that my NB healer doesn't need any more heals (naturally!). Thus, I just think it would be great if we could set up the ability bars to be character-specific (just like the outfits), rather than account-wide. Rapport, as others have posted about, is tough to gain! That's why I try to pair my chars with the comp that will fit with what they do in the game.
In recognition of the fact that not everyone will feel the same way about such suggestions, and that some may be much happier with an account-wide style "set-it-once, no-more-hassle" style approach, I think it would be awesome to simply have an option or options in the settings to be able to select companion outfits and skills as account-wide or character-specific. After all, several different addons allow for this type of setting to be adjusted (e.g., ActionDurationReminder, Combat Metrics, Inventory Insight, Dolgubon's Lazy Writ Crafter).
Those are my thoughts/requests! Thanks to the ESO team for the great content and all the hard work you put into the system.
If I see farther, it is by standing on the shoulders of giants - Sir Isaac Newton