Checked the description of the SD16_A modules in both of the controllers:
http://www.ti.com/lit/ds/symlink/msp430f4250.pdf
SD16_A, input range: Vi - Absolute input voltage range: AVSS-0.1V AVCC
http://www.ti.com/lit/ds/symlink/msp430f4784.pdf
SD16_A, input range: Vi - Absolute input voltage range: AVSS -1V AVCC
Are those values different for the two MCU's or it's some error in the description?