IC Sydney is the better option for a first time visitor, I'd say. Close to everything in the city, plus transport.
The rooms are a little uninspiring, and the bathrooms fairly old school, but the views from the better rooms are fantastic. Personally I really like the Eastern Harbour View rooms, looking out over the length of the harbour towards the ocean. The club lounge at the IC Sydney offers what has to be one of the best views in the IC world. Food is decent, nibbles more than full meal in the evening, but service is great.
Double Bay is a great little spot, a wealthy suburb with lots of boutiques and cafes. The hotel is good, rooms are fresher and more modern and yet still a little bland. From the hotel it's a short stroll to the ferry wharf, from where you can get to Circular Quay. A lovely way to get around but overall probably a spot better suited to the second time visitor.
DB is also the winner for breakfast, if you're dining in, the IC Sydney is often rammed and definitely not IC-worthy. Having said that, unless breakfast is included, head out of the hotel. Sydney breakfasts are great if you find a good cafe.
I wouldn't stay at any of the Holiday Inns in the city unless you really want to save money. Most are in need of a proper refurb. Crowne Plaza at Coogee is good, but again perhaps better for a second time visitor.