Can anyone shed some light on Memory Care vs. assisted living vs LTC for someone with dementia “on and off.”

Have you reached out to them to have your dad evaluated as to what would be the best "fit" for him?
You could tell the Social Worker or Director that you are going to tour other facilities and you would like to get their input first since he currently resides there.

NOW ..to the where he should be..
How well can he manage on his own? Does he need help with ADL's (Activities of Daily Living)? If he can manage well then Independent living might be an option but as he declines you will either have to move him to Assisted Living or they may just charge more for what they have to manage for him. If he can not manage then Memory Care would be the best option.
And if there is a possibility that he would walk out of the facility then Memory Care is the best as they are generally locked units.

And face the reality of it there is a good chance no matter where he is it is not like home and he probably will complain.

By the way if he is a Veteran check to determine if the VA can help in any way.

First off, I doubt your dad is going to be 'happy' ANYWHERE, frankly, because at this age, and in this state of mind, none of them are too thrilled in general. Secondly, a diagnosis of dementia means it's permanent, and likely to get worse, never better. Even though your dad's memory issues may be 'on and off', his dementia is constant. It can show up in many, many odd ways, too, not just with memory related problems. My mother is 92 and lived in Assisted Living (ALF) for 4 years and liked it quite a lot. She had friends and participated in many activities, went on the mini bus to lunches out and rides in the mountains, until vertigo became an issue, and she started falling a lot and going downhill quickly. She came down with pneumonia this past May and spent 5 days in the hospital and then 20 days in rehab/LTC. During that time, her dementia was terrible and she was scoring very low on the MoCA tests and even seeing mice running on the floor when there weren't any. She also became wheelchair bound during that time, due to all the falls and very bad neuropathy. In reality, she SHOULD have gone into the wheelchair at least 6 months earlier, but fought it off tooth & nail. Anyway, that's a bit of back story about my mother. So, the ALF refused to take her back after her stint in rehab was finished. Between her cognitive decline AND her physical decline, she'd be too much for the ALF to handle with a 20:1 ratio (or thereabouts) for resident to caregiver. They agreed to take her in Memory Care, however, for $2K a month more. She went from a studio apartment with kitchen in the ALF to a large bedroom (like a fancy hotel room) with a huge bathroom in Memory Care. The difference? 10 times more CARE in Memory Care with a 5:1 ratio (or thereabouts) for resident to caregiver. My mother needs that care, however, because she needs a lot of assistance getting from wheelchair to chair/shower/bed, etc. She's already fallen in the shower in the second week she was there. The downside? 90% of the residents are in MUCH worse mental shape than she is. They are asleep on the chairs or in another world, trying to get into rooms that don't belong to them and things like that. My mother is definitely the sharpest resident there, and she hates it. She calls the others "stupid" and "nuts" right to their faces, believe it or not, and I'm hoping she doesn't get kicked out. There are lots of activities in Memory Care (what my mother calls 'baby games' and 'baby arts & crafts projects', movies, etc) and they even go on outings in the mini bus. There are 24 residents in her facility, so it's very small. They all hang out in the great room where they eat, watch movies & do projects. There is also a small garden that they have access to.

So, there is your comparison. My mother feels she was better off in the nursing home where she was for rehab, but it's WAY more expensive and personally, I don't agree with her. There were plenty of other dementia residents there, too, but she 'forgets' when it's convenient to do so. She will tell everyone else how much she LOVES it in Memory Care, blowing smoke up their butts, so I'm not sure HOW she really feels. In the end, my only concern is that she is safe from harm, safe from wandering off, relatively well cared for by people who like their jobs, and somewhat happy. Notice I use the word 'somewhat'.

Don't overthink this. Keep in mind that Memory Care is ONLY for people who REALLY need a LOT of help and/or monitoring for being a wander risk. A last resort, in other words. If your dad qualifies for Assisted Living, I'd place him there in a HEARTBEAT, especially if there's a Memory Care attached, in case he needs it down the road. Dementia can be VERY slow to progress, too, so he may not be in need for quite some time. As far as activities go, he either will or will not participate, you cannot control that outcome. He may make friends with some old men and they can hook up to play cards and whatnot. Who knows?

I ran out of space, so here's my parting statements: I wanted to expand on saying that dementia presents itself in odd ways, not just with memory loss. My mother acts in agitated ways; she in constantly in motion in her wheelchair & can't sit still; she gets very angry & frustrated, yelling and cussing sometimes. She has no filter on her mouth anymore (even less than she's ever had before) so she will call people ugly names to their face, things like that. She also has no concept of time. There are 2 clocks in her room, but she either can't read them or doesn't understand what the 'time' means. Or which day of the week it is. Yet she can give you the gory details of some slight that happened to her 50 years ago. Some days you can barely hear her, her voice is so low and mumbling. Other days she's speaking normally. So........it's a vastly changing landscape, dementia, and something to keep an eye on. People tend to think Oh It's Just Short Term Memory Issues but it's NOT.

Anyway, good luck with your decision! I wish you and your dad the very best.

I think your dad doesn't sound quite ready for MC. When my MIL was in AL it had a "base price" where there were no services added (like laundry, meals, medication dispensing, etc). So you could request additional services as your dad needs them and the price also slides up. There was no kitchen in her apartment, just a sink and microwave and fridge so she ate in a community dining room and she so she had to come out of her room 3 times a day (or they came and got her...I can't remember). Yet I think it will still be up to your dad to go out and participate in ways but don't have any expectations. It may take him a while to adjust. Also, wherever he lands make sure the community offers MC and hospice so that if it ever comes to that need, you won't have to scramble to find it and won't have to up-end your dad when he is least able to tolerate it. Good luck!