Kashmir Shaivism (KS) rejects the Advaita Vedānta (AV) theory of eternal and independent ignorance. In Kashmir Shaivism, avidyā and māyā (illusion), are Śakti, They also believe in infinite souls and liberation. But liberation is not by knowledge alone as there are two ajnana in Kashmir Shaivism.
In Kashmir Shaivism, bondage is real and maya is also real. Advaita claims bondage is unreal and maya can neither be said as existent nor non-existent (Sat Asat), because these are mutually contradictory terms. Hence, Sankara has called Maya to be existent- non-existent-indescribable.
In KS, bondage is a play of Sakti. Shiva through Mayashakti (which limits the power of knowledge and activity) becomes bonded and becomes a jiva.
in AV, bondage is unreal and is beginningless,
In AV, no action is done by Atman. In KS, Atman is also involved in action.
From the book, Vedant And Advaita Shaivagama Of Kashmir by Dr. Jaideva Singh
The text below has been paraphrased as the differences are listed in 10 pages in the book.
The Nature of Absolute Reality
AV: the absolute Reality is simply Jnana
KS: it is prakasha-vimarshamaya, i.e. it has both jnatritva and
kartritva.
The Status of the World
AV: The world, according to Shankara, is mithya or false. It is simply
an adhyaropa or adhyasa or false imposition on Brahman due to ajnana
or nescience just as a snake is a false imposition on a rope.
KS: the world is an abhasa, but abhasa or appearance is real. The
abhasas only prove the glory and richness of Shiva. It maintains that
parinama-vada and vivartavada are not the exhaustive theories of
manifestation. Manifestation is brought about by the Svatantrya of
Shiva
Atman in the Human Body
AV: According to Shankara, atman in the human body is only
sakshi-chaitanya or witnessing consciousness.
KS: Atman in the human
body also is spandamaya. It has always the characteristic of jnana and
kriya
Difference in the Upayas
Vedanta: shravana, manana, and nididhyasana are the only means to
liberation.
KS: four upayas, viz. (i) amipaya, (ii) shambhavopaya,
(iii) shaktopaya, and (iv) anavopaya.
Difference in the Conception of Ajnana
Vedanta: avidya or ajnana is removed by vidya or jnana, and when this
happens, there is mukti or liberation.
KS: There are two kinds of ajnana, viz. bauddha ajnana and paurusha
ajnana. Paurusha ajnana is inherent in the paurusha ; bauddha ajnana
is intellectual. By vidya only bauddha ajnana can be removed, paurusha
ajnana will still remain. Such a person will only be landed in blank
abstraction. He will not realize shivatva or divinization. Paurusha
ajnana has also to be removed. This can be removed by Shakti-pata
which comes about either by diksha by a Self-realized guru or by
direct divine grace.
Difference in the Conception of Mukti or Liberation
The ideal of mukti in Vedanta is kaivalya or isolation just as in
Samkhya-yoga. The only difference is that in Samkhya-yoga, it is
isolation from prakrti, in Vedanta, it is isolation from maya.
The ideal of mukti in KS is shivatva-yojana or being integrated to
Shiva.