I like Summoner, but my personal issues with it as a job are:
1. We are a DoT class/job and a Pet class/job, but the 2 have no interaction besides Contagion which is why Garuda is infinitely more useful than Ifrit.
2. Pets have no tactical value. They are relegated to basically being a second auto-attack.
I would suggest giving each of the Egis a DoT/Debuff consistent with their elemental alignment. Having these DoTs interact with Fester would also help with pet/Summoner interaction.
Ifrit - Burn: DoT w/Strength Debuff
Titan - Rasp: DoT w/Defense Debuff (I would say Vitality, but that only affects max HP).
Garuda - Choke: DoT w/Accuracy Debuff (or Evasion debuff)
Leviathan - Drown: DoT w/ Mind Debuff
Ramuh - Shock: DoT w/Dexterity Debuff
Shiva - Frost: DoT w/Intelligence Debuff
etc.
I also think that in order to make Ifrit competitive with Garuda, they need to change one of his skills to better match the power of Contagion. In the spirit of ARR's Summoner, I would suggest something that interacts with DoTs such as a Debuff on the mob that causes all DoT effects to have an increased Critical Hit rate for a set amount of time.
I think if/when further Egis are introduced, it would be nice to see them have some tactical advantages over one an other, while remaining balanced. I think it would be a terrible idea to have Leviathan have anything healing-related. We are a DPS job and we should stick to that. I'm quoting myself from the Leviathan-Egi speculation thread:
Anyway, that's my 2 cents. ;-)