The Big Bus

No. Just use an ordinary bus.

Thank you!

It's your choice - it's not cheap and you will hit traffic. But they will go past the "sights" and it's a very popular low maintenance option for lots of people after an overnight flight

There isn't one public bus route that will encompass anywhere near the same amount of places so whilst there are advocates for that, you aren't really comparing like for like

What day of the week are you landing?

When I was in London in 2017 and 2018 I found the Hop on Hop off bus to be very very slow because of traffic during the week. (Actually all the buses are slow because of traffic) Not as bad on the weekend.
So I would suggest if the weather is ok and it is a weekend then take the Hop on Hop off bus. On weekdays…. Maybe not
but I disagree on the suggestion for a regular bus. They don’t really help you if you want an over view of the city. The routes of the tourist buses are designed to go to tourist locations not for usefull commuter transit lines as such they are usefull to go somewhere but not to get to see anything and get a feel for the city.
If you want to do a buss do the tourist buses and if the weather is good it up stairs and enjoy the view while the the automated voice tells you what you are eyeing and what you are coming up to.
Also keep in mind that they have night tours that can be interesting, they are no HoHo but it is interesting to see the city at night and less traffic issues.

An overnight flight? The gentle vibrations of the bus. Good chance you'll be napping on the upper deck.

To help fight fatigue and possible jet lag, you're better off getting outside in the sun and being on your feet. Take a walk. Have some breakfast or lunch and check into your hotel as early as possble.

Aside from the fact that I find the little streets often more interesting than the big ones the HO/HO bus would run down, if I sat down on a bus on my arrival day, I would surely fall asleep.

London Bus Route 11 used to be THE one that went past all the big name sights. Unfortunately that has now been re-routed after Victoria, and you now have to change onto the 25 at Victoria to continue east, which reduces it's functionality.
This is one of those questions which will always "spilt the camp" as to what is the "best" thing to do. Also The Big Bus is not the only HoHo bus in London.

We rode on the Hop on Hop Off Bus on the day of our arrival. We were nodding off the entire time.

I guess it depends on the person.
On my first trip in 17 we landed dropped our bags at the hotel, walked to the underground then took that to Tower Bridge (as much as you can). Walked along the river a bit then had lunch. Then grabbed the HoHo Bus to get an idea/view of the city. After that it was dinner and called it a day,
But I can see that some would not stay awake.

That being said yo each their own.

As transport between sights the tour buses are pretty useless as they run at too low a frequency and cover the area with a number of interlocking circuits making journey times long and unpredictable.

Doing a single route tour is rather expensive and will only show part of London.

You can sweat value out by doing everything they include- walking tours, river "cruises", doing all the circuits etc. This might take up too much time.