I really feel you on this, being a first-time mum and already thinking so carefully about your birth experience shows how much heart you're putting into this, and that anxiety about the labour room is so valid and understandable.
I haven't personally seen either of these two doctors, but since NUH is closer to home and you were already leaning that way, that proximity can actually matter more than you think when you're heavily pregnant or in early labour. My honest suggestion would be to book a first consult with Dr Biswas and just have an open conversation about your birth preferences and your anxiety, because how a gynae responds to that very first honest chat tells you a lot about whether they're the right fit for you lah.