Depending on where you stand, Vote Wisely can mean Vote WP or Vote PAP. Thankfully, thus far, no one (in my immediate circle) has used Vote Wisely to mean voting for all the other kacang putih parties that are NOT WP, nor PAP.
The WP-er intones "Vote Wisely" and means that one's decision should be based on...
(1) Growing a serious opposition Just-In-Case the PAP fails in future
(2) Growing a critical mass of opposition in Parliament so that issues are more thoroughly debated
(3) Giving some sensible alternative policies a chance to see the light
The WP-er is telling you to vote with your head and not allow PAP to frighten you into voting for it, for fear that the whole country will go to pot.
The PAP-er intones "Vote Wisely and means that one's decision should be based on...
(1) workable policies (e.g., small businesses are pressing for MORE foreign talent, not less and reducing reliance on foreign labour means that there are Singaporeans who suffer)
(2) a government that has deep and wide international and governing experience
(3) a government with good mastery of economics
(4) a government that does not take under table money
The PAP-er is telling you to vote with your head also and not allow the WP (or the other oppo teams) to stir you to hate the PAP for no good reason.
In essence, the term "Vote Wisely" says nothing and but means everything to the person who exhorts it of you. Cute, right?