First of all, it appears that the OP'er is confusing Advaita for all of Vedanta.
Next, what Buddhism would the OP'er like to compare against Advaita? There are realist and idealist schools of Buddhist philosophy each of which is irreducibly irreconcileable with each other. They themselves try to refute each other. So, to simply ask for comparison of Buddhism vs Advaita is not well-defined.
Next, the differences between Buddhist schools of thought and Hindu schools of though are steeped in issues related to epistemology (how do we know what we know), metaphysics (what is really out there, if at all) and then consistent with the position adopted in epistemology and metaphysics, each school tries to provide a view on soteriology/moksha/nibbana.
I have mentioned many times in the past that unless one is well-versed in these issues, trying to understand the differences between the schools is beyond one's ken.
All that said, perhaps the OP'er can clarify where exactly he/she would like to compare and contrast Buddhism (which school?) and Hinduism (which school?)
In any case, the OP'er can start by looking at the following threads and trying to follow the train of thought:
Advaita vs Yogachara:
http://hindudharmaforums.com/showthread.php?t=10137
Nyaya vs Dinnaga/Dharmakriti on empty terms
http://hindudharmaforums.com/showthread.php?t=10146
Uddayanacharya (Nyaya) vs Buddhist theory of momentariness
http://hindudharmaforums.com/showthread.php?t=8197
Brahmasutras' refutation of Buddhist realists:
http://www.swami-krishnananda.org/bs_2/bs_2-2-04.html
Brahmasutras' refutation of Buddhist idealits:
http://www.swami-krishnananda.org/bs_2/bs_2-2-05.html
Regards.
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