who is the doer? and which is better karma yoga or samkya yoga?

In general sense we all know about what ego is. it is the feeling of i as different from rest. this i called ego makes one think that the action is performed by him. also the law of karma says because of our action we get the respective results. but is it really we who act?
bhagavan says in geeta to arjuna that "prakrirther kriya manani gunaih karmani sarvashah ahamkaraa vimoodatmah karta aham iti manyate" meaning , those actions that are performed by the three gunas that are ingredients of this prakriti , are imagined by the foolish atman loaded with ego as performed by himself. in reality the jeevan has no power over prakriti. the prakriti is controlled by rta or cosmic order . " tvam eva pratyaksham brahma vadishyami, rtam vadishyami" . the prakriti has three gunas satva, rajo and tamas . this jeevan that wrongly thinks it is the body is controlled by the gunas of prakriti and hence its action.
Bhagavan continues with the statement " Bhoktaram yagnatapasam sarvalokha maheshwaram, suhrudam sarva boothanam gynatva maam shantim ichhati" the lord krishna is the sole enjoyer of all the sacrifices and actions. also he is the primodial cause of all activities--" eshwaraa parama krishna sachidananda vigrah anadi adirah govindah sarva karana karanam" --mentioned in brahma samhita.
the atma , because of karma gets associated with prakriti and is controlled by the gunas. hence its action is not by its free will but because of the nature of its gunas it is controlled by. but the atma because of grace of the lord alone, can break from this bondage by bhakti and prappati.
this does not give us freedom to commit violence thinking, "i am not the cause of action" because, till our ahamkara is caught with samsara and we feel that we are our body , all the merits and demerits of action will cling to us. " ayuktha kamaa karena karma phale ni-bhadyate"
the person who has not realised his self as a sesha to narayana ,will, because of affection by the results of activies, get attached to the results and again become controlled by tri-gunas. the path of karma yoga is to slowly detach oneself from the results of activities. thus karma leading to gnyana and further to bhakti is the right path. " sanyaasam cha yogam cha ni shreya sakara ubhauv , tayostu karma sanyaasat karmayogou vishishyate" --- of both karma yoga and samkya , both are fruitful but of the two karma yoga is superior and easier.
also as said by yagnavalka maharishi" kayaane vachaa manasah indriyerva budhytmana va: prakritersvabavath, karomi yadyat sakalam parasmi narayanaayethi samarpayaami" with my body, speech , mind and buddhi and other organs , conditioned by prakriti, whatever actiion i perform i do it for the sake of narayana and let the results be for him alone.