1. If you use dragon kata, anti-magic katas, crane kata etc, you are stronger than traditional style: you lose nothing but you have spirituality etc.
2. If occasion is such that you want to use tiger or octpous.
Instead of tiger you will have to use viper and you lose 4/1 -4 ac, quite unpleaseant but not fatal.
Octopus or Tiger - is by itself a hard choice and it depends on a particular situation. Since you can use only one kata at a time, it's not correct to say you have a double loss.
And elemental kata (of course it does not add any resistances or weapon flags) damage types are a good compensation. Yes you start fighting with 'shocking bites' or something like that.
3. You lose fourth attack but the skill contributes little to power.
4. Vibrations are more costly: 23 base mana instead of 20. This results in doing 8 vibras at a cost of approx 650 mana instead of 565 for traditional monks. 9 vibras for traditional monks is 725 or something.

5. You gain extra damage reduction and life regen from spirituality, perm invis kata, magic damage types for many occasions, double mana regen, 25 damage reduction from stone skin (instead of 16 from regular pills).
Is it worth 4/1 -4 ac for all those cases when you want to use tiger kata, and extra 70-90 mana for cases where you need to vibrate a tough mob? Dedice yourself and choose your style. If you cannot live w/o ability
to have extra 4/1 -4ac for special occasions, then choose traditional style.
Tristan schemonks gain additional things: protection vs good/evil - something traditional monks will almost never have except mb boots with prot evil, which, again, you have to wear instead of -20ac 2dr misty boots.
Also they gain fly, improved invis, pass door kata, again, quite handy.
All monk styles are close to each other: unlike say barb warrior vs barb shaman, all monks do the same stuff. So just choose what's more dear to you and go ahead.