Never heard about hand cut and machine cut. As per my experience here both are halal. but have little confusion here that is it allowed to eat machine cut or not.
الجواب وبالله التوفيق
The conditions of Shar‘ai Zabiha do not get fulfilled in machine slaughter, which is the reason why it is considered incorrect. In addition to the other conditions for Zabiha to be considered valid, one of the most important and basic requirement is to recite Bismillah while performing the voluntary (or controlled) slaughtering. In addition, one must apply force during the process of using a knife for slaughtering. It is mandatory that both of the above conditions are met through the same person. Therefore, such an animal will not be considered halal, where the recitation of Bismillah is from one individual while the actual process of using the knife is performed by someone else.
(Fatawah Qasmia Pg.145, Vol.35)
واللہ اعلم بالصواب