Which is better?

Depends on the condition, both physical and mental. Assisted living is likely to be more comfortably. Both tend to be staffed with minimum wage workers.

My grand mother is 85 years old. She is physically disabled due to accident. She is also suffering from memory related problems from few months.

You might have to look at nursing homes then. If you go that route, look at as many as you can, and try to get there around dinner time, and notice what kind of meals they have and whether they are getting the help they need. Notice which ones smell the best (seriously). Ask about the staff to patient ratio. Fifteen patients per staff member is the worst allowed in NM, but ten to one isn't really good. Ask about visiting hours. Ideal is whenever you want to visit. I would not trust and place that only allowed a few hours a day. I would almost think they had something they didn't want you to see.

You can also check out assisted living and apply the same standards. They will certainly evaluate her before accepting the admission. If they feel up to it, it might be a good thing to try.

I hope you're in an area where there's lots to choose from. Good luck.

Thanks for your suggestion roger.
Will it be affordable for me, because my financial position is not so strong.

I'm not able to answer that one. You might check into Medicaid in your state, or look into other state help. I think Medicare also offers some help, but if so, it is very temporary. Also, not a lot of facilities around here will accept either one.

In Albuquerque, NM, monthly rates seem to run from $4,000 to something above $6,000.

Assisted Living Homes with Nursing Facility.