I am staying at the Sheraton as I write. Chose the Sheraton solely on price; the Westin was close to double the rate, on our Corporate Rate program.
The Sheraton provide a Mercedes Limo service to and from the airport (about 45 minutes) for NT$1700 (about US$60). On arrival at the Lai Lai Sheraton the receptionist phoned the duty manager who personally checked me in at his desk in the lobby. I noticed the word "VIP" highlighted in yellow on the registration record. Since I'm not, I assume that Platinums are treated this way. He told me that I had been upgraded to a suite, but the hotel seems to offer no other perks, like free breakfast and free drinks and hors d'oevres that are offered, for example, at the Hong kong Sheraton.
The suite, on the 10th floor was spacious, with a good sized living area, and a nice bedroom, with king bed.
There was a large fruit basket, and a gift-wrapped box of Taiwan candies as the amenity.
The hotel is about 20 years old, I believe, and has an open atrium plan. There is a large cafe on the lobby level, serving a huge and widely varied buffet for breakfast, lunch and dinner, at least three bars, and some other specialty restaurants.
It is conveniently situated next to an MTR (subway) stop.
It is my first time at the Lai Lai, but I've already booked it for my next trip to Taipei in two weeks time.