First, let's expand each set of parentheses:

(a-3)(3a+1)
= a(3a) + a(1) - 3(3a) - 3(1)
= 3a^2 + a - 9a - 3
= 3a^2 - 8a - 3

(2a + 3)(4a - 1)
= 2a(4a) + 2a(-1) + 3(4a) + 3(-1)
= 8a^2 - 2a + 12a - 3
= 8a^2 + 10a - 3

Now, we can substitute these results back into the original expression:

(3a^2 - 8a - 3) - (8a^2 + 10a - 3)
= 3a^2 - 8a - 3 - 8a^2 - 10a + 3
= -5a^2 - 18a
= -5a(a + 3)