Seems that you are asking for mechanical differences, not flavor ones. The ones that I remember (and having in mind that I don´t have complete psionics
- Psions tend to be fairly specialized if constructed from level one onwards. Telepaths tend to end with a large, often redundant array of [mind-affecting] powers; kineticists will know a large ways to blow you up. There are ways to powergame around this, but playtest indicate that this is the case for many psions
- Within their specializations psions are often better, in a round-by-round comparison, than any other caster.
- Though they know a limited number of powers the power point and augmentation system and the power themselves allow great flexibility.
- Psions pay for excelence in their chosen field/s and flexibility with lack of stamina. They must carefully control the power points spent, because they fly quicker than you would think, quicker indeed that any other caster spends spell slots.
Minor aspects are:
- Psionics powers that can be used to buff others are very few, unlike arcane and divine magic. Psions can however buff themselves quite well.
- Arcane magic´s best defenses tend to rely on miss chances, invisibility, and similar effects (and can cast those effects on others); the psion´s best defenses boost their AC and hit points (and can only manifest those on themselves)
- Psionics lack good battlefield control spells, certainly nothing of the caliber of Wall of Force or Black Tentacles.
- Psionics´ save-or-die-spells are lacking. Actually, if i´m not wrong, there´s only one power in the XPH that kills directly, and it´s Telepath only. There are other save-or-be-incapacitated spells, but generally arcane magic is superior in this regard.
- Psionics blend aspects of both arcane and divine magic. They can blast and can heal (themselves, again)