Well remember that there were two civilizations that were Tai-speaking that rose from the ashes of Khmer rule:
1) Sukkothai
2) Ayuthaya
The first civilization was Sukkothai and was created and founded by the first Tai king , King Rhamkamhaeng the Great. He would influence the creation of the smaller states of Chiang Mai, Chiang Rai, and also the mountainous Tai state of Lan Chang. In fact these smaller northern states maintained their Tai ethnic identity tho adopted Khmer court culture and style of governing, evening religious practice --- Thervada Buddhism instead of Mahayana Buddhism.
I will say this tho, while the nothern Tai states of Sukkothai , Lan Chang, Pitsanulok, Chiang Mai, Chiang Rai and Ayuthaya spoke in their Tai dialect, the state of Ayuthaya was the largest of these. Ayuthaya also had a larger number of Mon and Khmer people who lived and mixed with the Tai invaders. They all spoke in Ayuthaya dialect of Tai. In fact in its height of power, Ayuthaya had conquored the smaller states of Lan Chang, Chiang Mai, Chiang Rai, Putsanulok, the Malay states of the south, Cambodia and part of the burmese shan lands.
Yes you are indeed right that in the latter half of the 16th century the Tongoo dynasty of Burma had threatened the Empire of Ayuthaya. In fact the Burmese king Bauyinog was even considered by Burmese, Thais and even Manipurese Indians as "The Conqueror of Ten Directions" because of his ability to subjugate various ethnic territories. The Burmese defeated the Ayuthayans in the 18th century and burned their great capital of Ayuthaya, but their control was limited to no more than a decade or so.
The Burmese governor of Ayuthaya was killed when the Siamese patriot named Taksin rose to power and rallied the people to wage a war of resistance. The Burmese were ejected by the end of the 18th century and Taksin 's heir had founded the current Chakri dynasty that now rules Thailand. While Burma would be destroyed and subsumed by the British in the 3 ango-burmese wars, the Siamese were able to expand their power the longest. This is why, my friend, I say that the greatest land based powers in the region were the Siamese / Ayuthayans and the Vietnamese / Dai Viets.
I would even argue the opposite. I will not deny that the Burmese Tongoo Dynasty was indeed effective at being overlords and to an extent had wielded clouts on their satellite states and had them field men to do their external affair fightings. The Burmese armies that fought and conquered Ayuthaya were not all Burmese you know; but actually composed of soldiers coming from Arakan, Manipur, Assam (South Asia), from Lan Chang, Pitsanulok, Malay sultanates of Johor and Songkla Pattani. You see the Burmans used politics and encouraged the tributary states of Ayuthaya to abandon Ayuthaya and join Tongoo Burmans to drive a force into the center of Ayuthaya in a pincer-like attack: a force from the north, a force from the south and a force by sea.
As quickly as these confederation of states and ethnic lords were composed together, so too were they divided--- quickly. This is why any and every single Burman invasion into Thailand / Siam always failed because the Burmans never really tried to integrate their newly conquered territories. That or Siam was just too large to control.