Conceirge class has bigger staterooms/verandas. You do get better service. choice of pillows, bottle of campaign, fruit, flowers, etc. The best advantage is priority embarking and disembarking. A Suite is usually even more room with a butler and extra services including a shower and a tub. The butler will serve you afternoon tea in your stateroom, help pack and unpack your cases, but there is an extra grauitity to pay when you have a butler. In conceirge your breakfast is brought to your stateroom, whilst in a suite not only brought but the table set out for you, similarly if you wish dinner in your stateroom instead of that evening going to the main diningroom or a speciality diningroom.
Conceirge was introduced as the middle ground between a normal stateroom and a suite without too much extra cost. I must confess I was not aware NCL did this grade, it was I believe introduced by Celebrity and now available on Royal Caribbean [who own Celeb]; Princess; Regent and Crystal. Next year we will be Concierge on Solstice then a Suite on the Century to celebrate our pearl wedding anniversary. Hope these points help.