I've stayed at both the Shangri-La and Le Meridien within the last year. I was pleasantly surprised by the Shangri-La; my room was quiet and well-appointed, the staff was helpful, and the lounge was quite nice. The restaurant breakfast was quite good, with a large selection and decent quality on most things (baked items were a little underwhelming).
I was not very happy with Le Meridien. I had last stayed there about 10 years ago, at which time I found it cold and dated. I needed to be in the area for work and decided that I'd give it another go for the SPG points instead of staying at the Shangri-La. Its now even more dated (I'm sure it was very contemporary in the 80's) and I don't much like the "modernist" style; both the public spaces and the rooms didn't feel very comfortable. My room was also rather noisy, as the windows didn't seem to block out noise from outside the hotel, even though I was on the 7th floor). Lastly, the breakfast was very disappointing for an Indian high-end property. Limited selection and rather poor quality. If you choose between these two, I'd say the Shangri-La is significantly better.

If you can handle being a little farther away, I'd suggest the ITC Maurya. I had a great stay there a couple of years ago- my room was outstanding, the staff was very helpful, and the breakfast was great. My wife will be there later this week; I'll add an update if it sounds like things have changed from our last visit.