If Rank 5 Telekinesis gives Amu the power of Accelerator, yet Illusion can beat Accelerator..... what does that say about the strength of Illusion in comparison to Telekinesis*?
I've got very little idea of what you consider to be a reasonable or in-scope feat for any psi skill, but throwing some ideas out there:
Interesting ideas, though if 5 dot psi skills are in broad strokes some what equivalent to lv 5 raildex abilities especially with specialities, then that might be thinking to small for them. Also I'm not sure one should be thinking about what beats what and rather what a particular skill could do for what you want to achieve.
To put some of my own ideas down on this,
--- Abilities that have some level of confirmation and/or equiv in Index/Railgun universe. So presumably the least speculative ---
- Telekinesis - Accelerator, is Vector control, the broad ability to influence the vectors of anything that has a vector... or thus anything that has a direction can potentially be influenced by this. This may thus include alternate physics.
- Illusion - Dark Matter, the ability to create anything including alien physics and construct it in to forms that do things based solely on the limits of what you can imagine and think up of.
- Teleportation - Asport, Teleportation. The moving of things around. Though in base concept it should actually contain space/time manipulation as such, as you can't otherwise do that. And that would be the ability to change the shape and form of base reality. Arguably in extreme this doesn't just let you teleport then, but also change distances and the shape and number of paths between places.
- Mind Control - Mental Out. At core the ability to manipulate and extract information out of any intelligent system, up to and including vast networks of it. Total control of any intelligent systems in extreme and in theory a pathway to super intelligence among other things.
--- A bit more speculative at times, so might get the base concept of it wrong, but I think they still make a fair bit of sense. ---
- Thermokinesis - If you extrapolate from base concepts then heat control is an aspect of Entropy. Which at core is that almost any kind of existence, with in our physics or otherwise, has the tendency to move from an Ordered state to a Chaotic state. Entropic control presumably would allow one then to do things like Stasis or change of how ordered
(cold) or chaotic
(hot) something is.
- Biokinesis - At core Biology is self replicating nanotechnology. So Biokinesis in extreme is the creation of life/(self replicators) in what ever configuration one wants them to be. In extreme may hold potential for exponential growth so long as sufficient energy/resources is available.
- Clairvoyance - The ability to see anything, anywhere when ever one wants. At extreme this means one can gather information from likely very extreme ranges. Basically know anything one wants to know from any place one knows of. If there is a more core way of seeing this I'm not sure fully sure what it would be, but perhaps total information awareness of local space? You may not comprehend what you are aware of though.
- Empathy - At core this this should be the comprehension of beings and the ability to simulate them, at least in part. In extreme total comprehension of any being?
- Mental Range - Most likely the distance ones mind can interact with directly with out shenanigans. in extreme with specializtion may well span the entire world, or maybe even more then that. In essence the area of total control?
--- Less sure of what these would be in this case, so pretty speculative. More information needed really. ---
- Precognition - The ability to either gain information from the future, or calculate what will happen from current information. Unclear how well this would translate to some kind of physics... so not sure what to make of this in extreme, though obviously one can predict some level of the future, especially if combined with Max Clairvoyance. It really isn't clear what this would be in extreme.
- Astral Projection - To project ones self in what ever one views as reality. Where Clairvoyance lets you see anywhere, this lets you project something there instead. Create a local presence? Duplication? Not sure what this would be in extreme either, though perhaps the ability to spam yourself at an opponent?
- Dreamwalking - It seems like some kind of ability to traverse an alternate realm? But if so what kind of realm? Mental? Real? Both? So one option in extreme then would be the ability to traverse any kind of realm?