I think it's worth it - but be warned, it's addictive! Ever since we have had our first concierge experience we haven't been able to go back to a "regular" room!
It's been a couple of years since our stay at AKL concierge, but we did have a good time. The lounge is spacious and the concierge CMs went above-and-beyond to make our stay perfect. Once you reserve your concierge level room you can email the intinerary planning office (IPO) and they will arrange any tickets, dining reservations or other pre-bookable services on your behalf. Definitely let them take of your ADRs since they have access to additional availability which you might not get if you call yourself.
One potential problem with selecting AKL concierge is that you are not guaranteed a savannah view - you might be allocated a pool view. If you really want a savannah view it would be a good idea to email the IPO and request this specifically so they can try and meet your request. Also, you should note that the concierge lounge doesn't actually overlook the savannah - it looks over the lobby instead. It's impressive, but I think it would have been nicer if they built it so it overlooked the savannah....
You do get an extra special benefit by staying concierge, and that is the ability to book the sunrise safari. It does cost (I can't remember the pricing, sorry), but it is a great experience - you need to be up at around 6am but you get a really up-close and personal Kilimanjaro Safari ride. There's an evening version as well (the 'sunset' safari) but I believe this one is considerably more pricey....ove $100pp I believe.
Even though we probably won't return to the AKL, because we felt it was a bit far out from everything and the rooms weren't overly spacious, the one thing that stood out was the number of special activities and events they have going on. In addition to the safaris, there were tons of neat activities for children and lots of guides and tours of the hotel for adults.
You can save $$$ by having breakfast in the lounge, bu otherwise the snacks are great additions to lunch and dinner. It's really nice to have the convenience of free drinks as well, and there are nightly dessert offerings which are wonderful.
The main benefit of concierge, in my opinion, is the level of service. We all know that Disney CMs are, on the whole, great. However, concierge CMs really go above and beyond and from our experience they have done literally anything to meet our needs. Need a same-day reservation at a booked up restaurant? They'll get it. It's the little things, too - my DS asked about chocolate milk when we were staying at the Polynesian, because they didn't have any out in the lounge. Within 30 mins they sent a few bottles to our room! DD and DS also kicked their new ball into the lagoon! The concierge CMs tried to get it "rescued" but had no luck. The next day they had a new ball waiting for them in the room when we returned. Obviously these things aren't guaranteed, but from my experience they really mean it when they say "have a magical stay" - and they work hard to make sure everything is flawless. Go for it!