Furryfurry, like what the sisters here say, if cost if not an issue, going to private could have better support from ther gynae. I can't advise what is the private service like for IVF as I did mine in KKVF under Dr Loh.
In KKIVF, you only see your own gynae 3 time throughout the whole IVF cycle, i.e. during the first consultation, ER and ET. The rest would be through the nurses and other more junior doc ( not Dr Loh). E.g. you did your blood test at KKIVF, the nurse will call you abt the result but you don't get the print out copy of the result unlike when I was in TMC, nurse will call you to inform you the results and at the same time sent you by mail the blood test results with the doc's signature and written words saying it is normal. So you are assured the gynea has reviewed the results. Of course if you have any queries or concern you can email Dr Loh anytime, and he may answer your email if it is an impt issue. So if you are ok with not seeing your own gynae so often through out the whole IVF process, you can choose KK as it is cheaper in cost. I spent around $8500 for my fresh cycle and there is a $3000 govt grant.
The most impt is that you are comfortable with the doc and how the IVF cycle would be carried out.