a point of view from a fresh grad. fresh graduated engineers are actually paid rather well in sg compared to most other jobs. if u graduated from nus/ntu u'll probably start between 2.5k to 3.5k a month. its nothing compared to front office positions in banks, but remember that these positions dun all go to business grads. if u are not a dean's lister or a first class, u'll can forget about being hired and u'll probably start at around 3k at some other position as well.
glamourous banking jobs are a lure to all fresh grads. even top students from engineering go into banking. but don't expect these jobs to be comfy. they are often high stress with long hours. remuneration is nearly always comensurate with (1) the quality of the degree u have; (2) the hours put in on the job and (3) the experience u have.
other countries may pay their engineers better. but if ur thinking of going overseas then ur not going to go far armed with just a local degree. again, the better paying jobs go to grads from harvard, yale, stanford, cambridge and oxford.