What additional am I getting for $3,000 for Alzheimer's facility?

What you should be getting is better staffing ratios. You want to find a place that has no more than 8 patients to 1 aide, for both first and second shift. Fewer aides are needed on the 11pm-7am shift since patients are sleeping. You want to find RN's and LPN's on duty at all times, supervising the aides. You want an MD on staff and a Psychiatrist readily available.
If they want $3K more, they need to explain the more service you get.

Mac, every area of the country seems to be different with what is available and what it includes! I was able to keep my Mom in an assisted living memory care facility for the length of her final illness. In this area, the AL's do not have a nurse at night. Since my Mom was in relatively good health, this was not an issue for me. There is often just 2 aides on the evening 11-7 am shift for the entire facility. (60 residents at my Mom's place.) On the bright side, the aides were supposed to check hourly on each resident. So, if someone fell, they would not be alone for more than an hour. (I am guessing that check up wasn't always done, but . .. ) My personal theory is don't pay for more than what is needed. The memory care assisted living facility I chose for my Mom was far better than ANY of the nursing homes in my area. In 2013, the memory care place for my Mom was $7200/month. Nursing homes in my area at that time were between $10,500 and $12,000/month

Macmcfarland, the main difference is the amount of "time" a caregiver would be spending with your wife.

Having paid caregivers from an Agency coming to your home, your wife would get undivided time and attention.

Living in an Alzheimer's facility, your wife would see the Aide first thing in the morning and again at bed time. The Aide would also pop in during the day to see how your wife is doing.

There are pros and cons to living at home, and living in a facility. It all depends on what is best for your wife.