Most weeks that I watch Chelsea, Hazard is the best player on the pitch and it isn't even close. He is far more consistent than Sterling and I don't mean individual moments in games like you have picked out, I mean a telling contribution over the full course of 90 minutes. For example, last week Sterling should have had a pen but he was poor for the majority of the rest of the game. The Palace game was his worst game in 12 months bar his goal. Against Spurs he was ok and Everton he was poor. The only game in those you have mentioned where he played well in addition to the individual moments was the West Ham game.
You mention Hazard yesterday and yes he was poor (after the opening 25 mins) and lo and behold they don't win the game. He is the heartbeat of that side. If he doesn't play well, they are nowhere as good a side. Unluckily for us, Hazard plays well most weeks. I would go as far as to say that if he wasn't at Chelsea they wouldn't be top of the league or at the very least they wouldn't be walking it. Sterling has nothing like this influence over our performances. I would swap them in a heartbeat.
I would agree with you, I think hazard is the much superior player right now and only the most biased fans would disagree with that. He is just a more naturally gifted player than sterling and I very much doubt sterling will ever reach his level in terms of technical ability(touch, dribbling, passing, finishing etc) and to be honest very few players in world football are as naturally gifted in that area as him. As you said, he is not the most productive in terms of numbers and his influence on chelsea is not normally seen when looking at pure numbers. He's basically their main/only creative force and is one of the few players in the league who can make something happen out of nothing. His play is more of that of a playmaker than a winger. The problem with Hazard though is that because of how gifted he is with the ball, I don't think he ever tried or thought it was important to improve his game when he isn't on the ball (positional, movement, tactical awareness etc). This means that when you starve him off the ball in games, his influence drops considerably for his team and is also a factor as to why I doubt he will ever produce the kind of goals and assists numbers to reach the level that some of the very elite attacking players are at( i.e bale,neymar,ronaldo). All those players have that tactical side to their game which makes them as dangerous with the ball as without it.
That is an area that sterling already possess and is his strongest suit. Meaning that as you noted, there will be a lot of games where he will not be consistently involved or influencing a game but then in a blink of an eye you will see him through one on one with the keeper with a clear goal or in a position to set-up one. The first goal against barcelona at home this season sums this up perfectly. The team till that period was getting outplayed, heads were beginning to drop for some of the players and barcelona were in full control of the game. Then one misplaced pass and a couple of seconds later the ball was in the back of the net. If you watch that goal again, not only was his positional sense perfect in case they lost the ball, but his anticipation of the play ahead of time was superb. He received the pass and then also had the awareness to set-up gundogan for a simple tap-in and change the complex of the whole match at an important time in the game. That goal came about in small part because of the misplaced pass but mainly because of his intelligence and movement/timing of run without the ball and then also knowing what to do with it in a high-pressured moment. There have been many instances of that this season including his goal against crystal palace in the fa cup which also came about because of his movement and anticipation of the play ahead of time. There are very few wingers in football regardless of age with that level of tactical intelligence.
So while for the short-term it would totally make sense to take hazard over raheem, its when you consider their ages and start looking at it with a long-term view then are you able to understand why some would not. Just think of how much sterling has influenced a game at key moments this season (assist vs barca, goal vs arsenal) and how much intelligence he has to his game already and it begins to get scary to actually think what he can/will be able to do when he reaches hazards age. Here you have a young player whom even in seasons where he underperforms like last season, he still manages double digits in goals/assists. Imagine how dangerous he will be then if or when he becomes a more decisive player which comes with more experience and also improves his finishing and composure in front of goal even just a little bit. Not to add this is also a player who though may not be at the level of hazard technical wise, is actually very capable technically and better than at least 90% of wingers in the league in that side of his game.
I came across this stat last week
which not only shows how intelligent he is to find himself with the ball in the opposition box that many times but also how much he has on the technical side to be able to complete that many take-ons in an area of the pitch which tends to be very crowded. Now no one can predict the future and sterling may never improve the technical side of the game to reach a very high level. But for what he contributes to the team right now and the coach he has with him who seems to have full trust and confidence in his ability, I'm willing to bet that it won't be long till you see sterling produce and influence games at a very consistent level in terms of goals, assists and creating chances.
