How does the historical jesus compare to the jesus ...

 Historical Jesus is the same Jesus of today. No difference.

The answer you will get to this question depends greatly on who you ask. A figure like John Dominic Crossan and others affiliated with the Jesus Seminar would say that the historical Jesus is nothing like the Jesus of Christian theology and not really much like what we have in the Bible. This has some distinct weaknesses just from the standpoint of historical studies though.

The question assumes that there is a distinction, this assumption may not be warranted however. What are the sources we use for determining the historical nature of something? Usually we rely on written attestation, in the case of Jesus this will be primarily found in "gospels" written about him. We must judge whether each particular historical record is reliable and worthy of acceptance. The earliest gospels are those four contained in the New Testament, they are the earliest and most reliable historical accounts of Jesus since they were written nearest the time of his life and they were written by individuals who seem to have been probably eye witnesses to the events recorded in them, with the notable exception of Gospel of Luke which is more of a historical compilation of eye witness accounts.

With that being said the historical Jesus is most probably the one revealed in the Bible itself. So then what do we make of this likelihood? There are elements which some want to dismiss as mythologizing or super-naturalization but when multiple witnesses attest to the same and similar events we should be intellectually honest and admit that perhaps our assumptions are wrong, rather than the eye witness accounts. In this regard I am referring to the naturalistic assumption against the supernatural. So if we are willing to lay aside that assumption we then begin to see that the Jesus portrayed in the Bible is not only likely to be the same Jesus that actually lived in history but also that he is the Jesus of Christian theology because Christian theology is built upon these biblical accounts regarding Jesus and his works.

For the Christian there can be no distinction and for the person who is intellectually honest any distinction is false. This leaves only two choices: (1) either acknowledge and accept the truth of who Jesus really is/was/etc., or (2) disregard it all as a lie and believe instead, against all evidence, that Jesus never existed and that all the evidence is merely an elaborate fabrication. Those are the only two roads the a thinking person could possibly accept and only the first is really reasonable.

P.S. - I am a conservative Christian attending a conservative Christian seminary but judge my answer with an open mind and I think you will be inclined to agree with my assessment. 

The direction of the "historical Jesus" is to focus more on two sides that are not being used in the field of "theological Jesus" - History and Archaeology!

Studeying dipper into questions of history in the New Tetament, in Josephus Flavius and other sourses as well as the results of archaeological excavations. For example, how did Maria used a Miqve (a Jewish ritual bath), the only way to answer it is through the finds from 1st century AD sites like Gamla in the Golan or Yodefat in the Galilee. More information you can get at the books: "Excavating Jesus" and "Jesus and Archaeology" as well as in the documentary "Echos from the Ancients".

I would like also somewhat agree with Dubbs in that what we have to go on Jesus as far as "historical jesus compare[d] to the jesus of theology" is a silly way to put it. History is not based on digs.  History assumes that what people write is true and in this sense history is not a science.  Perhaps in certain schools though they have given labels to a discrepancy between what is found and what is recorded in text, but really this is all semantics.  I think you are trying to ask a question though and I am going to assume you know what you are trying to say and not limited by the "academy" you are coming from.  There is in fact discrepency in "Gospels".  One writer who attests to this is Pagels (writer of "Origin of Evil")  Church cannon on gospels was decided by a vote around 400 AD. There were testaments of Thomas and Mary that have been discarded because they contain a different Jesus.   Perhaps a bit more Gnostic one.  It appears in the Mary Magdalene version Jesus seems to have a relationship with her that is a bit more intimately revealing then the other followers.  In the dead sea scrolls there are apparently documents containing accounts of other "unknown" prophets doing things that Jesus did but with slight differences in the story and done about one hundred years before.  I have not translated these texts myself and I can't know for sure if they are real or not, but Elaine Pagels she really seems convinced that these dead sea scrolls contain a realm that is off cannon, and off the main story, but date back to the same period and conflict and contradict other texts.  There are also conflicts in ancient texts in strange stories recorded during the period that show a strong influence of the good and evil polarities of Zoroaster's religion from Persia and has a lot of angels who become the focus of interest.  The angels become almost personalities close to g-ds in pagan religions and it is no wonder that many of these scrolls were rejected by both Jewish and Christian cannon.  What is clear though is there was an evolution in the story, similar to the way every religion in the world seems to have a flood story and those flood stories appear to be recorded around the same time in a different way.  I don't base any decisions based on these testaments any more then I would base my opinions on the testaments that are cannon.  In the end your spirituality comes from inside and unfortunately for us isn't objective and provable at all.  That is why it is a faith.