The Buddha describes four 'exquisites.'
Careful reading will show that the three different translations will yield three different modes of practice.
Read the Sutta
The meaning possible to draw from the three translations (including Bhk. Bodhi's) is different in ... um ... exquisitely subtle ways each of which will yield a radically different form of practice.
At a certain point in your studies it will be vital, at the least, to understand that there are differences of opinion as to what is being said. I will try and be helpful.
Four of the five 'stockpiles' (rūpa, vedanā, saññā, saɱkhāra) (khandhas) are to be dealt with:
Per Woodward: A monk is possessed of the power to penetrate the subtlty [sokhummāni] of body, feeling, perception, activities; he beholds no other power more excellent, he aspires for no other power.
Per Bhk. Bodhi: A bhikkhu possesses supreme exquisitness [sokhummāni] of form, feeling, perception, volitional activities, he perceives no exquisiteness more excellent, and does not yearn for any other exquisiteness.
Olds: A beggar has beheld a most exquisite [sokhummāni] shape, experience, perception, own-making, cannot conceive of a higher exquisite shape, etc., and aspires to no higher exquisite shape, etc..
The problem with Woodward's translation begins and ends with the fact that there is no mention of any sort of power in the Pali. He is giving us an interpretation in reliance on his understanding of what is said in the commentary: [Per footnote: "Comys. read sukhumāni and define as: 'knowledge of how to penetrate the subtle characteristics.] By this he has, I believe, short-circuited the intent of the sutta and deprived the reader of the little itty bit of visibility of the absolutely essential piece of knowledge it provides. (I'll get to that in a minute and you can judge for yourself.)
The problem with Bhk. Bodihi's translation is that he has the bhikkhu possessing (having become in himself, most exquisite in) these forms, etc. which perceptions would justly be called vanity, self-deception and manifestation of a belief in self. He footnotes; My [insert in italics]:
"Mp's explanation [see quote above] seems to me problematic. I would identify exquisiteness of form with the form perceived in the fourth jhāna, exquisiteness of feeling with the neither-painful-nor-pleasant feeling occurring in the fourth jhāna and the formless attainments, exquisiteness of perception with the perception in the base of nothingness, and exquisiteness of volitional activities with the residual volitional activities in the base of neither-perception-nor-non-perception."
Putting aside that these are just guesses (he says "I would identify" not "These are"), Bhk. Bodhi is trying to identify what is the exquisite form, etc. being spoken of. If the attainment of a certain state had been the point of the sutta, it is certain that that would have been stated. There are much more direct and less uncertain ways to get the states Bhk. Bodhi mentions than leaving it up to the subjective judgment of the individual.
But the Buddha says:
These are the exquisites.
In some way what we have in front of us must be made to be those exquisites.
The meaning of a sutta needs to be found in the wording as it is found ... for the most part, except where there is an obvious connection between suttas, a sutta will have been delivered to an audience which might in it's lifetime hear that sutta and only that sutta.
Further, if the prose part of the sutta is to be taken alone, Bhk. Bodhi's translation is making the Buddha say that these four exquisites, attained by the bhikkhu, are the most exquisite exquisites, which is not the case.
The most exquisite form of a bhikkhu does not compare to the most exquisite form of the Buddha, for an example. The most exquisite form of a bhikkhu at one minute will not be the same as his form will be in the next minute so it will not be possible for him to form the non-desire to have any other exquisiteness since he doesn't have the one he thinks he has in the first place. ... and for many other similar reasons this cannot be the meaning.
My suggestion is that the prose part of the sutta is an instruction in how to identify when one has perceived forms, etc., in a way which requires no further exploration of form to know that one has seen sufficient to understand form as it is.
"Having seen the best, I can leave the rest."
It is not necessary to have seen the most exquisite (the absolute best) form of all forms, and it is not necessary to have perceived form in any particular state, and it is not necessary to have become form in any particular state, to have reached the point where a form is perceived as exquisite.
It is simply necessary to have seen such a form as satisfies.
That is, to re-interpret the quote from the commentary: having seen forms in a way that satisfies provides a basis for insight into the characteristics of forms. Or one might say gives the power to penetrate the subtlties of form.
That is the sum total of the sutta, but there is a verse that follows which possibly clarifies and certainly confuses the meaning. It says:
If he knows the subtlty of form, and sees various things about feelings, perceptions and activities, the monk lives in peace in his final body having conquered Mara.
Per Bhk. Bodhi:
Having known the exquisitness of form, and seeing various things about feelings, perceptions, and volitional activities, the bhikkhu lives in peace, bears his final body, having conquered Mara.
Olds: Knowing exquisite form, and understanding certain things about experience and perception he knows that the own-made is painful and not self and aspires to peace, to bearing his final body and to conquering Mara.
Woodward and Bhk. Bodhi essentially agree, I dispute.
But the real problem here is that this is only one case of what should be four.
We should be finding here that: Knowing exquisite form, exquisite experience, exquisite perception and exquisite own making, and seeing certain things about experience and perception (and I would add 'form') he understands that the own-made is not self and he aspires to peace, bearing his final body and to conquering Mara
... or ... there should be four separate stanzas, one each for exquisite form, exquisite experience, exquisite perception, and exquisite own-making, each with a concluding set of factors.
My guess? The commentator who invented the explanation used by Woodward and objected-to by Bhk. Bodhi (but actually accepted by him in the form of the verses) inserted the verses intending to reveal the meaning, (that is, the verse is the original commentary). As commentary he would not necessarily need to work out all the variations.