...is it better to use highway 44, which starts near Kanchanadit and than via Plai Phraya or the old 401 route via Ban Ta Khun?

Definitely 44. It is a divided highway 2 lanes in each direction and hardly any traffic. Go unil it ends then turn left toward Krabi for about 1/2 km and U-turn for Phang Nga/Phuket. It is about 20 km further but you save time because no small towns and villages to slow down for. Drive is through mostly large oil palm plantations and there are many limestone outcropping type mountains around for scenery. No gas stations or toilets though, so plan ahead!

Thank you for good advice.

I was not so sure, because last time I saw a blue Phuket- Surat Thani bus on the old route. I guess it is shorter kilometre-wise that way and so they safe fuel costs.