Caledonian Sleeper vs Flying Scotsman?

The Flying Scotsman is just an ordinary service train, one of many in the day, to do the journey from London to Edinburgh. It just carries the historic name, although the new LNER timetable suggests that they have dropped all train names.
The designated Flying Scotsman is not even the fastest service of the day.
So it's the same as any other electric train on the route- fast, efficient and comfortable.
It would be useful to the OP for us not to get buried in semantics again (as we have in the past). On this route it is electric traction.
The steam locomotive 'Flying Scotsman' very rarely does special trains London to Edinburgh, and then at a very special very high premium price. Most of the time the locomotive is touring the UK visiting Heritage Railways.
Leaving aside the polarised debate on the merits of the current coaches, the Cal Sleeper (colloquially known as the Deerstalker Express) is one of life's great railway journeys.
Few things on rail beat leaving London at night, with dinner and a dram in the diner, having a night's sleep and waking up next morning in the majestic scenery of the Highlands with breakfast and a coffee in hand on the train.

Not exactly answering your question, but we took the Caledonian Sleeper from London to Edinburgh right before Covid hit us. Overall, it worked fine for us as it is nice to arrive in Edinburgh first thing in the morning for a full day of sightseeing. The train and staff were nice enough. My only complaint was that the bed in my compartment was placed between a wall end to end and the mattress length was 6’2”. I stand 6’4” and I was not able to stretch out as I normally prefer. Other than that, I would recommend the service.

Thank you, Jay MN. We are just beginning our research for a 2024 trip - we leave for France this month and are always looking forward to our next trip.

If you would fancy a vicarious train journey from London to Scotland , in the meantime , Watch this forty three year old version with Michael Palin , of Monty Python notoriety. - https://youtu.be/mYi1qLUAJJI

We did the Caledonian Sleeper Inverness to London route last May, and we loved it! The only downside was that I waited too long and we didn't get the double room, so we ended up with the Club room with bunkbeds. They were a little narrow, but we thought the mattresses were very comfortable. The rooms are tiny, so we spent the first few hours in the club car, having dinner and then coffee and dessert, while we watched the countryside fly by until it got too dark to see anything (11:00-ish). I slept in the upper bunk because the ceiling was a little lower, and I'm only 5', while my husband is 5' 10". It was a little challenging for me to get in and out of (my husband still laughs about the "rear view"), but other than that, it was fine. We had breakfast in the club car the next morning, which was pretty good, and included in the ticket price, and we got to enjoy looking at the scenery as we ate.

One caveat - if you're traveling with anything larger than carryon, the aisle to get to the rooms is very narrow, and the underbed storage isn't huge. We had watched a few YouTube reviews, so we knew to expect that, and we only had one carryon and a backpack each, so we were fine.

We thought it was a great way to combine travel time and sleep time, and for us, the cost was similar to what we would have spent on a hotel and (easyJet) flight, minus the day lost in traveling.

We travelled on the Caledonian Sleeper May 2022 and enjoyed the experience. We didn't take dinner in the dining car, instead buying something on the station and eating in the cabin. We are both short so had no trouble with space in the beds :-)

Our tickets entitled us to a visit to the lounge in Fort William, so we had ourselves a cup of coffee and used the time to get our bearings in Fort WIlliam since this was our first visit for more than a year (our 4th visit all in all).