One of the best things about char-x is the fact that everyone runs char-y. Whenever I see a plain charizard, I automatically assume it is a char-y (to my fault). And the key resistances that char-x has to char-y's weaknesses really make it stand out. Unfortunately, char-x suffers from some "solo mon syndrome" as he simply offers damage and not very much team support. This would be as opposed to char-y's team-helping sun.
One of char-x's major talents is its ability to output crazy amounts of damage. This of course has the benefit of damage. But unfortunately, it also comes at the cost of flare blitz recoil, further making char-x difficult to use. I suppose you could run fire punch, but the shift from 120 base power to 75 base power is noticeable.
A few hints I have for newer users to differentiate between the two charizards would be this: Look at team preview and if you see pokemon to abuse sunlight in the form of chlorophyll, weakening of water attacks (passive sun abuse), moonlight abusers, or other ways to abuse sun- you can probably assume it is char-y. However, if the team looks fairly regular/goodstuffsy then it might be char-x. Most likely as kale mentioned above, you will see a char-x come out late game for a sweep. So if they are hiding their charizard throughout the game, you can have a good guess it is char-x seeing as char-y likes to immediately mega-evolve and give sun support.
(Quick note: Some char-y's don't immediately mega evolve in the matchup against rain. This is so they can change the weather on a politoed switchin. In the matchup vs rain, not immediately mega evolving charizard does not necessarily indicate char-x).
The rest of this is about char-y, because more common :>
One of the things about countering charizard-y is that the pokemon that attempts to counter char-y has to have a reasonable matchup against char-y's fren chlorophyll venusaur. For example: this makes the would-be check terrakion slightly less reliable because venusaur can outspeed terrakion and put it to sleep or outright kill it. Some of the better mons I have found to counter char-y (and by extension venu) would be rotom-h and goodra. The former can only be seriously dented by venu's poison attacks or venu's sleep powder. Many players circumvent being put to sleep by running safety goggles or lum on rotom-h. On top of that, rotom-h can threaten both out with its supereffective stab.
Goodra stops the two by resisting fire attacks and being immune to grass attacks (sleep powder I'm looking at you). It also has a monstrous spdef stat which allows it to eat up any poison hits from venu. From there, goodra can threaten both with supereffective hits from its spatk stat.
Unfortunately, running these two char-y (and venu) counters means that you cannot run rotom-w or other dragons (too many ice, fairy, dragon weaknesses). I guess this just speaks to the metagame shaping nature of char-y.
About
BlankZero 's heatran, I find that it is not necessarily a surefire answer to char-y. This is because of the possibility of focus blast. Although I will not lie, I use fake out + sub tran (w/o ancientpower!!!) to stop char-y cuz I'm lazy :]
One of the fun tricks I have found in countering char is the water+ttar switch. How this works is you use a water pokemon as bait for a charizard solar beam. Then on the predicted solar beam, you switch into ttar. Your sand will make the charizard charge its solar beam, and also weaken the solar beam. After taking like 1 damage from a sand weakened solar beam, you can rock slide the char because it is forced to stay in and solar beam. Just a note, this tactic requires that they mega evolve on the water type. If your opp suspects this trick, they may save mega evolving one more turn so that they can solar beam ttar without repercussions. (remember, ttar switches in first, sand summons second, char mega evos third, sun summons fourth)
As for interesting char-y sets, I have experimented with overheat and tailwind as fourth moves (after heat wave, solar beam, protect). I find the former fun, as you can roast would-be checks. I also find it fun because the mon they are bringing in will most likely force you out anyways, so going to -2 dosen't matter since you are going to switch anyways. As for tailwind, it is cool but pretty lackluster. I never really felt that the extra speed helped. Perhaps it was because I used venu (*4 speed, gotta go fast) and was already fast or because just twind is bad on some mons ;].
Anyways, charizard is a cool pokemon with a lot of versatility that I don't use because it is inferior to mkanga :]]]]]]]]]
