Ironically, the Tanakh is in Hebrew, the Brit Chadasha is in Greek, and we have an english translation. So an assumption is made between the correlation of the thee... let's examine that correlation.
In Exodus 3:13 *(I AM)--- Hebrew: *(hayah)
*def.= (always emphatic) will to come to pass
or will become
In Mark 16:62 (same as the John 8 passage) I *am--- Greek: *(i'-mee)
*def.= (always first person, singular, present, and indicitive) exist
now notice that with the Hebrew (and this is the only place in the Masoratic texts this occurs) it is "I AM" (one word) being referred to as "will come to pass."
Now in the Greek (and this is only referring to the word "am") it is exists.(one more quick note, this "am" used here is a commonplace word amongst the Brit Chadasha)
So Yeshua was saying before moses I existed.
YHVH was saying I will become. "Become what?" one may ask.
YHVH will become what ever it is you need. Yehovah Yirah: the L-RD my provider
Yehovah Nissi: the L-RD my banner
Yehovah Tsidkenu: the L-RD my righteousness
Yehovah M'Kaddesh: the L-RD my sanctifier
Yehovah Rophi: the L-RD my healer
the list goes on and on.
YHVH will BE all of our needs. He is all in all. Now take note of I Cor. 15:27-28
"For he as put 'everything underneath his feet'. Now when it says that 'everything' has been put under him, it is clear that this does not include G-d himself, who put everything underneath the Messiah. When he has done this, then the Son himself will be made subject to him who put everything under him, so that God may be all in all."
The bible itself speaks that it is clear that Yeshua is not included in this G-d, who put all under Yeshua's feet. Yet we are under Yeshua's feet, and all will proclaim him as L-rd (adonai), yet he also proclaims his father (YHVH) to be his Adonai. As David said "My L-rd (adonai) said to my L-RD (YHVH)..."
This theme becomes quite common in the Tanakh. The L-rd (adonai) subjects himself to the L-RD (YHVH). This also happens in Rev. 3:12-14 as Yeshua declares "MY G-D" four times.
This idea is echoed in Jewish thought. We see the lesser and Greater Yud Hey Vav Hey. Often, in mystical writings, the lesser YHVH is referred to as the Metatron.
Of course, this is getting into very heavy kabbalistic views, so I'll just leave it at a few thoughts:
1) Are the two "I am" passages significantly related to each other after considering language contexts?
2) Does the Torah, Tenach, Brit Chadasha, etc support an equality between the entities of the Greater and Lesser YHVH?
3) Does the Tenach and Ketuvim Netzarim support an equality between Y'shua and his adonai?
These should be excellent starter questions.
Shalom,
Yafet.