Basically, this theory states, there are two forms of shikai: the "physical" and the "metaphysical". (I'm leaving bankai out of the question for the moment.)
The "physical" type of shikai has an active and perceivable physical effect on the world around it (ice, soundwaves, steel blades, huge whips, fire, etc). On the positive side, it's always useful, particularly when dealing with hordes of low-level enemies. On the negative side, when the shinigami is up against particularly powerful enemies, it can be dodged/parried/avoided, or even countered.
Examples of this type of shikai are: Yamamoto (who just pumps so much power into his that it can affect anyone), Hitsugaya, Kuchiki Byakuya (steel cherry blossom petals), Momo (fireball blasts), Ichimaru Gin (long blade), Ikkaku (power hit), Komamura (big power hit), Tousen (sound waves or blades), Ichigo (blasts of power).
On the other hand, the "metaphysical" type of shikai are basically hax. They have some sort of special effect, and quite often the user keeps quiet about what the special effect is in order to be able to use it more effectively. On the positive side, they seem to be able to affect an enemy of almost any power level, if they hit.
On the negative side, the "metaphysical" type of shikai carries an element of risk. It has some form of inbuilt weakness or way of avoiding its effect. The more powerful it is, the bigger the "risk" is. Most users of this sort of shikai try to minimise the risk by training to lower the opponent's chance of interference, keeping quiet about its exact powers, or choosing their fights carefully and using strategy.
To clarify what I mean, please consider the shikai that I would call "metaphysical" by this definition:
Aizen: Kyouka Suigetsu (yes, we all know what this one does)
Risk: if someone doesn't see the release, then it doesn't work on them at all.
Strategy: don't tell anyone what it actually does till after they've seen it.
Kira: Wabisuke (increases weight of opponent's weapon or body)
Risk: if you can't actually hit the other person, it's not much use.
Strategy: use tactics and kidou to lure the other person in for close combat.
Soi Fong: Suzumebachi (two-hit kill)
Risk: if the other person is too fast, or if she can't close with them (cf Barragan), then it won't work.
Strategy: increase personal speed so that she can close with the opponent and hit them twice.
Yumichika: Fujikujaku (drains energy)
Risk: while we haven't seen a specific weakness in this zanpakutou yet, I suspect that such a weakness does exist.
Strategy: don't tell the other person what it does till it's too late.
Ukitake: Sogyo no Pisces (absorbs and returns energy blasts)
Risk: if the other person isn't firing energy blasts at him, it's less useful.
Strategy: when fighting someone throwing ceros around, hit them first and explain later.
Shunsui: Katen Kyoukotsu (forces opponent into life-and-death children's game chosen by zanpakutou)
Risk: if Shunsui loses the game, he gets hurt and might even die. Also necessary to give some explanation of the game to the other person so that they'll "play".
Strategy: hope the zanpakutou picks a game that allows surprise strikes and cunning play.
I would note that in the above listing, it would seem that the higher the potential "risk" factor in "metaphysical" shikai (Aizen, Shunsui), the more powerful the shikai.
The "metaphysical" type of shikai may be what Yumichika means when he refers to "kidou-type" zanpakutou: I'm not sure.