I would like psionics but would like it to be different than magic. Dispel magic should not work against psionic effects and magic resistance should not count against it.
Psionic abilities should not be subject to line of sight / cover rules governing magic. If you see, perceive, or know of someone's location you can affect them. If a psionic wielding character sees someone through a windows, they should be able to use their psionic ability, even if an equivalent spell would not work because of line of sight and cover rules.
To balance the above advantages, and to create a distinct flavor, Psionics characters should be limited to a very small, select number of psionic abilities: telekinesis, clairvoyance, mind blasts, read minds, control person/beast, mind blank, ability to buff strength and constitution temporarily, etc. The focus should be on increasing the power and versatility of individual psionic abilities more than adding more abilities.