No, the wife is not equal to the husband and there is no obligation on him to obey her as there is upon her to obey him.
it would fall under the commands where the gender and the relationships have been defined. (Unless the wife is shunning the orders of the husband if it goes against the Shariah) And Allah, the Supreme, knows best.
As brother Noori clarified, in the general commands, the male includes the female. However, in specific commands, when the gender and the relationships have been defined, the "vice-versa" will not apply, for example in the following ahadith. If I were to order someone to prostrate before someone other than Allah, I would have commanded the woman to prostrate before her husband. If a husband tells his wife to keep carrying a load of stones from that red mountain to that black mountain, she must obey him whole heartedly. "(Ibn-e-Majah) "When a wife vexes her husband, then the houris of paradise utter curses on her saying, 'may Allah destroy you because he is with you only for a short time; he will shortly leave you to come to us." (Ibn-e-Majah) And Allah, the Supreme, knows best.
For example this hadith sharif of bukhari only mentions muslim man (mo'min) but includes mo'minah too عن أبي هريرة - رضي الله عنه - أن رسول الله - صلى الله عليه وسلم - قال(يقول الله تعالى: ما لعبدي المؤمن عندي جزاءٌ إذا قبضت صفيَّه من أهل الدنيا ثم احتسبه إلا الجنة))؛ رواه البخاري Narrated from Abu Hurayrah raDiyAllahu a'nh that RasulAllah sallallahu a'laihi wasallam said - Allah ta'ala says "when I take someone (or somthing) beloved from his world and he remained patient upon it, then the reward with me for my mom'min slave is nothing except jannah"
In quran usually only men are mentioned in ahkam, but both men and women are included in the application, the same would be the case in hadith sharif. We also need to qualify it with 'right shara'i displeasurment' otherwise many times both man and woman get displeased for something which is haram.
the meaning of the hadith says that, 'if the husband if displeased with his wife, then Allah ta'ala will not accept her worship.' what about vice versa and wife displeased with husband?