Uno is extremely easy for even young people. Fluxx requires fair amount of skill with English (even my father had problems, surprisingly). I think they both are casual games. There’s a few factors that affect this.
Fluxx is the epitome of a chaotic game. This chaos is amplified when there are several people. With two or three people, your play actually has a visible effect on your next turn; with six, it does not have too much of an effect. There’s some, but not enough to count on.
Uno has few variants that are played among the circles where I have played it: First is to draw one or two cards when you can’t play any, second is to draw up to three cards until you can play one (and immediately play that). The third is to draw cards until you can play at least one of them and then play that. The first are least unpredictable, the third most. Also, the number of players has a large effect: Usually it is possible to meaningfully affect the next player or maybe two, again depending on the rules used (stacking “draw”-cards either affect only the next player or each player gets one effect until all cards are used). As in Fluxx, the state of game can vary significantly between the turns of an individual player. This is almost the norm when there are many players.
Why do I think unpredictability is good? First, it reduces stress; you can always blame the luck and will often be correct. In addition, both games can take new players in midplay and not make a significant splash. Further, one can take a pause from the game when the others are doing their turns and often not a lot has been missed.
No death spiral
Fluxx tends towards equality among the players due to the numerous hand limits and keeper limits, as well as rules reset. Further, winning the game is always possible by shifting the goal, stealing or scrambling keepers (and the changing the goal), or just picking the correct keepers and playing them. If you’ve got no keepers, hope someone will put a limit on them. Fluxx doesn’t so much balance itself as it screws everyone equally and always keeps victory a possiblity.
Uno self-balancing in a very elegant way: The more cards one has, the faster one can get rid of them by playing many at the same time. Also, as one gets more cards, the chance of drawing cards that match them in symbol only increases. (People rarely forgetting to say Uno is also something of a balancing mechanism, though very weak one).
The lack of death spiral means that skilled players don’t seem to dominate, because they could be toppled at any moment.
Take any system where participants have turns, take some action during a turn, then wait for the next one (examples: Heroes of might and magic n, most rpg combats, ADOM, roleplay with a split party). How much does a single turn matter?
Number of actions
Obviously, the number of actions one can take are very important. If one can somehow get more actions or deprive opponents of theirs, such abilities often are extremely valuable. For example: Haste in D&D 3rd, reflexes in Burning Wheel. If the number of actions or action points that are used when doing anything can be altered, one would do well to start with a fair number of them. If everyone starts with single action, getting another is worth very much. If everyone has 10 action points, getting 1 extra is very nice, but won’t as easily break things. Getting 5 or more does break things.
There may be a chance that the actions one takes simply have no effect. High whiff chance is undesirable, because it tends to be frustrating (I want to hear a counter-example for this one). Further: With a significant whiff chance, the system becomes more chaotic; a given amount of play may give no results or be hugely effective, depending on luck. Obviously low number of actions and high whiff are a bad combination.
One has actions and does not whiff. What happens? In all examples I can recall right now the power of different actions (choices) is different. This may be balanced by different costs (in actions or other resources), different whiff chances (magic missile always hits), or other factors.
Memory may not be quite as obvious a factor as the others. In a system with long memory the effects of the choices one makes linger for long. They may change or weaken but one can easily see that a particular effect is there due to a particular choice made. System with short memory obfuscates these relations: The status of the system changes rabidly or radically. Or maybe there is a large number of choices made, so that the effects of single one are effectively buried. Or maybe there is a strong attractor the system tends towards, so choices tend to be lost as the attractor is approached again.
In roleplaying context: Traditionally, system has long memory with regards to character generation. Choices there count for a lot (hence the flames around point-buy vs. rolling and the tendency to let people do minor changes after actually playing a little). Character death is another event that games tend to remember for long.
Gamers try to avoid effects that are harmful and have long memory: D&D examples are level drains and ability drain/damage (prior to plentiful restorative magics). In the Mountain Witch the wounds that have duration for “rest of the game” tend to be nasty (this one is from experience), even if that duration is rarely more than three sessions. Generally speaking, permanently disfiguring a character is something that many gamers really dislike (exceptions abound). In some games, losing items is more harmful than character being wounded, because healing is fast and wounds matter little in the long run.
An interesting rules element
Whenever a player loses a conflict/roll (as suits the game and situation in play) any participant can suggest a permanent consequence, or at least one with long memory. If the player does not want that, damage time, for whatever values of damage the system recognises.
Example the first: A troll subdued the would-be trollslayer. Options: Take the harm (given the circumstances, may very well be death unless there is help coming) or take a semi-permanent nasty effect, such as a trollslayer cast into the river from which he is rescued with only his clothes on (or so the villagers insist), or the troll consuming the slayer’s right hand and leaving the slayer to die, not liking the taste.
Example the second: Negotiations with the high king. A failed diplomacy check. Options: Beaten up and thrown away from the castle, a humble apology (and charisma damage due to the humilation and loss of confidence), the ire and later assassins of the high king, losing some allies from the local nobility, being branded an outlaw, …