Hello.
Both the fields that is Neurosurgeon and Anesthesiologist are great, it primarily depends on your interest and your inclination towards the particular field.
Neurosurgery is the medical speciality concerned with the prevention, diagnosis, surgical treatment, and rehabilitation of disorders which affect any portion of thenervous system including the brain, spinal cord, peripheral nerves and cerebrovascular system. The main challenges faced by neurosurgeon is that brain is the most important and most delicate organ of the human body. Because of this there needs to be taken extreme care while operating in the Operation Theater.
The working hours are pretty high and the schedule tight. But at the end of the day you feel the satisfaction of saving others lives by giving your maximum effort.
Anesthesiology is the study of anesthesia and administering the same on patients, those needs surgical intervention as part of their treatment.
Anesthesiologist has a role to play in every surgery who is responsible for the dosage of anesthesia assisted to the patient. There are jobs available as a part time as well as full time.
Salary is obviously more in the part of Neurosurgeon than in Anesthesiologist.
Now I think you can take your decisions based on your priorities.

I hope that helps.

Wishing you all the best.