To let you know where I am coming from, know I taught in a school especially designed for kids with learning disorders where at least half of my students were severe ADHD cases for three years (and regular classrooms for an additional seven). One class was always severe ADHD only. I also have my own daughter and we are looking into getting her evaluated for ADHD, as she does express MANY of the symptoms.
First, I want to express that I know this is hard but as parents there are certain times when taking a deep breath and taking a little time off isn't a luxury but a requirement. Get some time away from it all to decompress a little.
Secondly, I would like to stress Brian White's point that making sure you listen and understand how he is feeling regularly is super important. Make time to have low-pressure conversation where he can express his feelings without judgement. It is important that he have opportunities to simply be heard. This will help build his feelings of trust toward you and help him become more self-aware. In fact, it is the best way to address your son's concern that you love the other son more. Listen, listen listen. Knowing you are listening will help build his confidence and sense of self worth as well as his ability to listen to you in exchange.
Some ADHD kids want to be in control and do whatever they can to be in control - even if it means being in trouble all the time. They'd prefer (on a sub-concious level) knowing they effected your emotions than to give in to being controlled. Giving him the opportunity to express appropriate control over some aspects of his life will start when you decide on some priorities related to exactly what you want out of his chores.
For example, is setting the table about getting it set or is it about teaching him to pitch in? If it is about teaching him to pitch in, try offering some options. Would he like to set the table or fold the laundry while you prepare dinner? Maybe he'd like to help with dinner by learning to measure out ingredients, or wash pots and pans so you can set the table. Make sure when you give options that both options work for you though. The second option should never be a threat. When it is time for room cleaning, you might try something like, "I need you to pick up all this clutter in here and put it away and bring me your dirty laundry. You can choose which you do first" picking up the laundry, or picking up the clutter.
My final suggestion is a little different and will sound crazy at first but please read on because it isn't what it sounds: Stop punishing him. I do not mean to just let him get away with it, instead what I mean is, make connections between his behavior and a natural consequence. For example, if he were simply a guest at your house and had bad manners when he came over to eat, you'd probably not invite him back. To apply this reality to your own family dinner table (where he needs to be invited back), if he is using bad manners (which includes complaining). At the first complaint simply remove his food and say, "oh, I'm so sorry you don't like it. Let me get it away from you." Don't offer him anything else either though. He can go to bed hungry or figure out how to reheat his dinner on his own later. It sounds mean, but he won't starve and he'll get the point.
When he doesn't set the table or help with dinner, simply don't serve him food. Say, "Oh, you wanted to eat too? - well since you didn't do your part in our family community today, I thought you were saying you didn't want participate in family activity" No warnings, just do it. He'll whine, say it isn't fair and make all sorts of a fuss, but calmly say over and over again that everyone has their job to do in order for it to work for everyone to enjoy dinner together. Again, he won't starve if he misses dinner now and again and he is learning an important lesson - He may be a prince (mine is certainly a princess), but even a prince has his responsibilities.
Same goes for other chores. The "punishment must fit the crime." If you've asked him to dust the family room and he didn't do it (so you did, cuz you didn't want to nag or wait any longer), he doesn't get to use the family room. "Sorry, I know. I agree that it is really sad and we will miss you during our family movie viewing. You should be with us, but only people that help keep it clean, help to make it a mess again". Don't be sarcastic or biting at all, be genuine but make it clear that the rule still applies, "Maybe next time you'll have done your share and we'll be so glad you are back" You get the idea.
If it takes him three hours to clean his room. So be it. If taking so long means he can't go on an outing with you, be sad about it, "Wow, what a bummer you'll miss out. We really want you to come. I'm so sad you didn't get your room cleaned". It sounds like you are already applying a "first things first" approach to this, but instead of it being a "punishment" that he doesn't get xbox, tv . . . simply make it a, "you can play when" kind of a statement along with your empathy. "I know this is really hard for you. I'm feeling (insert emotion, sad, disappointed, frustrated. . . ) about it too. You can play video games when you show me you can also clean up after yourself."
These kinds of natural consequences can apply to A LOT if you let them. The main things are that you always stay calm and sympathetic, make time to listen, paraphrase and empathize, never threaten and do not give warnings. Simply let the consequences fall where they may and although you listen, don't negotiate (maybe with an occasional nudge here and there to the consequences). The reason for no warnings is that it sets it up to come across as a threat and/or punishment. It is also really easy (I'm guilty too) of suggesting the consequence and then not following through.
For more information read, "Parenting with Love and Logic", "How to listen so they'll talk and talk so they'll listen" and "Seven Habits of Highly Effective Families" You might also check out the Mecham Family and see if you can sign up for a workshop about control and consequence at www.schoolathomeeffectivley.com.