That's a tough question haha But for me, I chose the gynae that I wanted first, rather than the hospital and since she only delivers at Thomson, I chose Thomson. I guess the facilities for both hospitals should be on par as both are private hospitals. But Thomson is very crowded! And if you drive, the parking at Thomson is really a nightmare. My hubby always give a black face whenever he has to pass the car keys over to the valet people. Not too sure about East Shore though.
Why dont't you sign up for the free hospital tours at both places and see which one you are more comfortable with? They will show you the delivery suites and the wards etc. Might have a better idea after that.
Hope this helps! Good luck in your search...