I am a regular user of bigbasket.com and I do find them quite reliable. They have always been on time and the staff(customer service and delivery) are well trained by Indian standards. I love the fact that they have delivery slots - they always stick to the slot.
They could do with improvements on a few things though.
(i) They always run out of things on my grocery list. I am yet to receive 100% of my order list.(ii) Their co-ordination with their delivery people is quite bad. I once rescheduled my order and while they accepted my revised time, they forgot to tell the delivery team who obviously brought up the order as per the initial time slot.
These are minor issues though so I intend to continue to be a loyal customer.