Y-intercept with Dummy Variables?

[Apple Tan]

Hi

I have got 2 equations (See attachment).

A) Basically, I just want to know what is the difference of a
1) model with the variable "trend" interacting with my dummy variables (Eqn 2)
2) model with the variable "trend" alone (Eqn 1)

B) How do I check which is a better model?

Thank you