Stayed at both (GH pre-renovation) and do note the GH is actually just off what people would consider Orchard Road. It's a less than 5 minute walk to the action though. Additionally, while public transport access (MRT) is not an issue at both, I loved that the Andaz is directly connected to the Bugis MRT which made things extremely convenient and allows you to avoid the outdoor heat you will have to endure at the GH.
Obviously, if a club lounge is of importance to you then it's no competition as the Andaz has no club lounge.
Other than that, I loved the Andaz for the location (Bugis) and the views you got from the rooms. This is in despite an extremely disappointing interaction I had with a front desk agent. Orchard in my opinion is the most overrated location in Singapore and has not much to do other than high-end luxury shopping. Even for luxury shopping, I prefer the Shoppes @ MBS anyway.