This is the subject of dispute between R. Saadyah Gaon and the kabbalists, on the one hand, and ibn Ezra and Maimonides on the other. According to Rasag (Emunot ve-de'ot 4:1), man is greater than all other creatures by virtue of his free will. This is also the view of the kabbalists:
Man is greater than the angels in that he was given inclinations, and
obliged to contend with vital questions and his bodily needs, even
with the seductions of the evil inclination, while the angels'
existence is static.
This distinction is famed for the names assigned in it to man and the
angel. Man is called "walking" (mehalekh), and the angel "standing"
(omed) (after Zech. 3:7). R. Meir ibn Gabbay stated that "The truth,
traditionally upheld in our
nation, is that the source and level of the soul [neshamah] is higher
than that of the ministering angels, and that it therefore has
dominion over everything that is below it" (Avodat ha-Kodesh, III, 5.
See also Tishby, Wisdom of the Zohar, 2:679.
(Source: Moshe Halamish, An Introduction to the Kabbalah, pp. 250, 352 n. 9.)
However, ibn Ezra (Exodus 23:20; Genesis 1:1) criticizes this view. Maimonides (Guide for the Perplexed 3:13) also maintains that man's place is lower than the angels. See also Guide 2:7 where Maimonides distinguishes between the choice of man vs the choice of angels.
The Midrash (Devarim Rabbah 1:12) states:
א"ר אבא לעתיד לבא עתיד מחיצתן של צדיקים להיות לפנים ממלאכי השרת והם
שואלים להם מה הלכות חידש הקב"ה היום, א"ר לוי בר חנינא ואל תתמה אף
בעולם הזה היתה מחיצתן לפנים ממלאכי השרת שנאמר (דניאל ג) ורוח די רביעאה
דמי לבר אלהין, שהיו לפנים מהמלאך והוא מכבה לפניהם האש
According to the Midrash, it seems that primordial and eschatological man are higher than the angels, but in the mean time the angels are higher than us.