This typically occurs in instances where players who do not play the same position are being compared. Any discrepancy you may see occurs because the tools are using slightly different expert bases.
The Who Should I Start (WSIS) tool compares players from different positions solely using expert rankings that have been submitted for flex rankings. The Lineup Assistant only uses rankings from experts who have also submitted QB, WR, RB, TE, flex, K and DEF rankings.
This results in the expert base for the Lineup Assistant being slightly smaller than that of the WSIS tool by a few experts. If you choose your experts for both tools so that the same expert rankings are being used for each tool, then you'll notice that both tools will choose the same player to start.