bus or fly from Tallin to Riga?

I'd suggest the coach. Lux Express has nice coaches and when you add all the airport faff that comes with flying it won't really save you much (if any) time.

Or the train at 1025 daily, guaranteed connection at Valga, all on modern trains, 30.50 Euro each.

There are sightseeing buses that take you and reasonable luggage between the two cities:

https://www.traveller.ee/tour/tallinn-riga-bus-tour

Departing daily from Tallinn, for €95 pp, it's a 12 hour excursion with several stops.

I enjoyed a similar sightseeing transfer between Vilnius and Riga.

Caution, however, that my Riga to Tallinn weekday transfer did not have the minimum number of people to happen. Knowing this was a possibility (it's very clear in their "additional info") I had bought a refundable bus ticket as a backup.

I had seen the sightseeing tour bus and would love to do it, but we need to arrive in Riga by dinner time because of my husband's work obligation. Unfortunately, train takes too long for our schedule.

Well, I don't recall that the bus scenery was "spectacular" but I did enjoy it more than the rigamarole of an airport. But then, I wasn't in any hurry.

I took a 4.5 hour journey with Ecolines (there was power at each seat) for €12 and enjoyed conversations with an Italian student traveling back to study in Moscow (in 2023!) and a Ukrainian girl traveling back to Estonia to visit family.

I took the Lux Express bus between Vilnius and Riga. The roomier seats. They were comfortable and in a 1-2 configuration while the front of the bus, the regular seats were 2-2. The coach had free wifi, a toilet and free coffee or tea (self service). It was a decent trip. Every seat in the premium section, which is at the back, was taken. There was some seatback entertainment but nothing in English.

When I was scheduled to travel from Riga to Tallinn a few days later, I had booked Lux Express again. But the morning of my trip, I was not in the mood to sit on the coach for nearly five hours. (I knew the scenery wasn't that amazing.) So I booked a last minute flight on Air Baltic. Both Riga and Tallinn airport terminals are easy to manage. The flight itself was comfortable and the crew friendly. It took less than an hour. The entire trip by plane was shorter than the entire trip by bus. I'm glad I made the change.

I took Ecolines between Tallinn and Riga and for me, the scenery was spectacular--I am inordinately fond of storks, and this was early May and they were everywhere--in fields, and in their enormous nests atop telephone poles and other platforms built for them. I had intended to nap during the 3+ hour trip but was happily transfixed. My first experience on a foreign bus and it was surprisingly pleasant and cheap, I definitely recommend it. I had an 8 am departure and was walking to my hotel in Riga by 12 noon.