There are pros and cons to each.
It really is a matter of personal choice.
It is possible to get 2 concierge rooms cheaper than some 1br suites when you are using some code or AP discount.
Right now the codes that are out for concierge rooms at AKL, for example, bring the cost down to $380 per room. A 1 br suite is $710. Pretty close in price.
We were trying to decide between 2 concierge rooms and a suite for our trip to AKL this fall. We decided on a 1br suite. That way, we can "live" in the living room area and sleep in the bedroom area. The master bathroom in the 1br suite also looks great with a huge shower. They also have a nice size dining table in the living area and a fridge and micro. The suite also works out better for us because DH needs to get up early a certain day and we can sleep in the bedroom and he can sleep in the living room or the opposite.
The above poster is correct, some suites do not come with concierge. The ones at AKL do. I am not sure what other resorts have suites that come with concierge.
My DH just didn't want both rooms to be filled with beds and he likes the living area of the suite better. He feels it will be more relaxing. I think there is a small bathroom with a sink and a toilet in the living area.
Hope this helps.