What's with all the trolls coming out of the woodwork in the past week?
Short answer- Depends on the individual fighter and the ruleset/scoring. Watch fast small guys like Keaw fight in K-1, his head movement is great, Attachai Samart, Lerdsila, Namsaknoi, list goes on.
You rarely have to worry about getting hit by too many punches in general in Muay Thai matches, especially in Thailand, most punches are long i.e. Jab Cross, and when you're close your hooks and uppercuts are replaced with elbows. You also have more options to deal with them like clinching up or countering with a kick. K-1 rules has considerably more punching than MT.
Like someone said earlier, the leanback/rockback is the staple dodging technique for most MT guys because alot of the strikes you're worrying about are kicks that come at that swinging angle.
You'll get a little slip here and there, maybe weave under a punch and circle away off the ropes ala Petrosyan/Souwer in K-1 rules.
Boxers only have two hands to fight with and defend with so having both hands free instead of one is in their best interest. Naturally, this exclusive attention to hands can be neglected more by Thai boxers. Just a different game.
MMA by nature restricts high volume full power kicks and long punch-kick combination flowgame that most Thai boxers and Kickboxers rely on, so naturally the striking would be more boxing based because being on one leg has dire consequences unlike in kickfighting sports.
Long answer- *will update with a novel when i get to a computer*
