The InterContinental (The Lalit Mumbai) is where I stay while in Mumbai and is actually slightly closer (100 metres?) to the airport (international terminal) than the Leela Palace. I prefer the InterCon’s rooms and actual building (recently refurbished rooms, many with wood floors and flat screen tvs and an impressive atrium) to the Leela Palace however the gardens at the Leela are very nice. The service at the Leela too is exemplary. The InterCon does not provide free transport unless you have booked the executive club floor but can pick up from BOM for a charge.
A bit late on this posting (and certainly late for any voting) I know, but have just recently joined the discussion forum.