All the authorised money changers (MC) in Singapore offer comparable rate, and definitely much better rate than the banks (bad move by the banks). Unless, you are going to exchange a large sum of money, the difference in FX rate will not effect so much.
If you are going to exchange a large sum, negotiate with the MC for a better rate than what is on display (otherwise you'd take your business elsewhere). They are likely to keep your business, but do your homework before negotiating so you know roughly what is your optimal rate.
Also, I have exchanged AUD to SGD on the day that has a higher selling rate than the previous day (worse off). I was able to negotiate the MC to match the rate of the previous day.
P.S. I said to the MC...."whoaah, yesterday rate was better. Match yesterday, can?" and they let me have the better rate.