The default go-to on Summoner is Garuda-Egi, and it is potent due to the ability to extend debuffs (which works with Bane and allows you to DPS with ruin in addition to your DOTs) as well as the range it has and the steady damage from it's primary attack skill.
The biggest crutch for a Summoner playing on gamepad is control of pet due to the cross hotbar and how wonky the pet controls are on them, but it's not enough to prevent a Summoner from playing on PS3/4 outright.
As far as damage goes, Summoner ranks among the top DPS in the game, though the degree by which is debated due to the inability to accurately parse DOTs.
The only standing issue with Summoners is the debuff limit on enemies during large group activities such as FATEs, due to evidence of a 30 debuff limit upon monsters and the incredible number of Debuffs that can be piled during popular activities. There is fear of this effecting Arcanist participation in Crystal Tower due to it being a 24 man run, but there's no active reference to work for yet, so it is a speculative fear at best.
In the end right now I'd say choice of which to play between BLM and SMN is a matter of prefrence. BLM hands down has the better passive crowd control with Sleepga, where Summoner can defer to their Titan Egi if off tanking is at all required. Both have a decently strong AoE game, though Black Mage has more damage potential per number of monsters due to the limit on how many enemies Bane spreads to.
Ifrit is far more useful on speed runs or where there won't be a prolonged battle. Ifrit for trash, Garuda for bosses, even Titan. Granted I haven't done Coil yet, but this seems to be a general rule of thumb.
Sleep is highly useful, but don't forget SMN has an equal duration Bindga, though it suffers the same diminishing returns as BLM. We also can pair it with Swiftcast, just like BLM can with Sleep. Pop your DoTs, run up and Miasma2, then Tri-Disaster and stand back and laugh as the numbers fly! The definition here, of Bane:
Spreads a target's Bio, Bio II, or Miasma to all nearby enemies.
Duration: Time remaining on original effect. Additional Effect: 15% chance that Bio, Bio II, or Miasma duration resets. Only available when under the effect of Aetherflow.
If there's a limit to the number of mobs, it must be more than ten or so, as I haven't seen it personally. Edited, Nov 1st 2013 1:10pm by Dallie