Upside of having two characters?

[Alistaire]

What exactly is the downside?

Also everything that people have said here but also maps, having your dex/int jobs on an elezen and str/mnd jobs on a roegadyn, that kind of thing. Not a huge boost but there's not exactly a huge detriment to running 2 characters.

[Sadana]

It's fun! (I have 13.)(maybe 14.)
You could always use the new character to refamiliarize yourself with the game and swap back later if you want to.

[Rikkustrife]

more ventures, can get twice as many tomestones

Plus it feels different playing different characters so it has some variety , and there is no reason not to

[Mattlex]

If you only have Warrior and Black mage levelled it is worth just starting a new class on the same character. There are benefits to having a second character but you will have to do a lot of the main scenario and GC stuff again to be able to ride mounts etc etc, I would only reccomend starting a whole new character if you plan on doing all those work arounds for lockouts etc people mentioned. Otherwise just start a new class, I found Archanist a fun class to play but you have many options without starting a new character.

[Fendred]

Having both male and female exclusive gear.

This. I will never have the lightning hair cut unlocked or lightning's outfit. Also, cascadier outfit can only be for one sex. To be honest though, male/female exclusive gear doesn't make a whole lot of sense when two people putting on the same kind of armor can have different designs. (What ever happened to the part of the dragoon armor covering the belly on the female model?! X.X).

However, if you intend to do the end game rep grinds or the atma -> animus -> novus questline, you'd be better off not making a second character. The time requirements on those things, especially when taken as a whole, are brutal.

[Mini_Me]

Not wanting your lalafell to look like 'Ted' when tanking or kicking somethings ass. I prefer a Rogayden for tanking, melee just doesnt fit with being a lalafell in my opinion.

[Riastrad]

This is a strange thing to do/ say but... I have 6 alts all with level 50's and relics for main jobs.
After I cap tomes on my main character for week (usually Wednesday night) I play another till I grow bored with them or cap tomes. It is incredibly easy to do so because of frontlines (not that I'm complaining). Granted, most of these characters are from 1.0 and had a head start on levels.

Pro tip: Place them in the same FC so that you can share items between them along with Gil. If your main ever gets low the quest rewards from the storyline will come in handy.

[SummonerSenah]

I liked seeing the different starts to the main story based on where you started. On my main I started in Limsa and on my alt I started in Gridinia. Also, one is a Miqo'te and one is a Hellsguard Roe, so they look very different. It was fun playing with the character creator. The biggest advantage to me personally was being an arcanist on both and taking one down the summoner route with full 30 in intelligence, and taking the other down the scholar route with 30 in mind.

[Veerne]

+ You can play more.
- You have to play more.

[Kayo]

Having both male and female exclusive gear.

This here is the only reason I have 2 character I play regularly (and am thankful that Lightning event is coming back). Not a big gear grinder so I couldnt care less about coil lockouts. Wouldnt level a whole other toon just to fill spots though I wouldnt mind if I already had one.

Im entry level anyway so the toons are in different servers. Also, later on, I would imagine another reason to make a new character is to just have a low level character to play with. Once you get all your class/jobs to high level you cant be a newbie anymore. Plus some players like revisiting the main story now and then... new race, new starter area maybe ....