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. In fact, it is the best way to address your son's concern that you love the other son more. Listen, listen listen. Then, tell him what you understood from what you listened to. Paraphrase him. 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.
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.