I have had a good experience with DELL service for laptops bought in India. Regarding a DELL laptop bought in US and brought to India, I think they can find your laptop in their database BUT not sure they will have all the config details available. That's what my experience was with my laptop that I brought from US.
Service is on-site as long as you have a warranty and the service is not charged. BUT as soon as the service warranty is over, every visit is charged and can be expensive. I don't think there should be any difference in charges if the laptop is bought in US.
Though if your US MODEL is not sold in India by DELL, then you could be have a big problem because service technicians will NOT be trained for that model and hence may not be able to serve you easily.