Considering I always find you a bit anti-united but that is a fair fair reasoning.
I love the club (bit too much sometimes which can come across as being harsh or overcritical when we're not doing well) .. but one thing I can't tolerate is bias
Hazard tends to terrorize opponents - when on form. Also, he is playing for a Conte team with about 7 defensive players and he's the main creative outlet (only one in midfield you could argue, at times). Sanchez on the other hand played for a far more open team - and an inferior one - where he also carried a goalscoring burden, knowing nobody else could do what he could when it came to end product. He also did it consistently. Far more consistently than Hazard, you could argue. As a defender, no idea who I'd rather face, but I'd also argue that the probability of a 'mare against Sanchez is higher simply because he turns up far more!
You could also argue that if you put Hazard in the Arsenal side, they'd never have won the FA Cups or made Top 4. Hazard is just not consistent enough and I'm not sure he could "carry" a team like Sanchez has carried Arsenal. His goal output isn't great (he says he doesn't bother about that part) and for all his occasionally mesmerizing dribbling, he can be a no-show as often as he can be a game-changer. He's something of a "luxury player" I suppose - in that when he purrs, he delights, but his lows are awful and he won't muck in as much as a Sanchez.
You're right in saying that the preference would vary by team. Some teams will benefit more from a Hazard. I just feel though that there are probably more teams that would benefit from a Sanchez. Has he proven his worth? Well, he's won two Copa Americas (against Messi, at that) and also been PFA Fans' Player of the Year twice. He's also won La Liga (Barca) and two FA Cups. Apart from the La Liga with Barca, you could make a strong case that he's been the main man for the other trophies. Wouldn't quite call that "unproven", to be fair. If you take only PLs or CLs, well, there's a lot that would miss out and David May would make a case to really be a superstar!
I think this narrative of Hazard rarely turning up is quite absurd. Him in his prime, with full focus and motivated failing to lead them to an FA Cup (which is a knockout - so not guaranteed but arguing he wouldn't be able to lead them to one) is also absurd. Also using goals and assists is not quite right as Sanchez is more goalscoring orientated and Hazard is more playmaker orientated.
Look I'm as happy as anyone that we have signed Sanchez and I would much prefer Sanchez at this moment in time than Hazard as I think Sanchez has the better mentality for what we need at this moment in time (he's been my dream signing for a long time) but generally even in games in which they're up against each other Hazard has generally looked the superior player despite Sanchez playing in the more attacking side. Hazard for being such a lazy player has to do an awful lot of heavy lifting for Chelseas attack and that is not being recognised by alot of fans in this thread.
Yes Sanchez has lesser team mates but he plays in a more attacking system and even at Barca. Even Chile are pretty much on the front foot whereas one could argue Hazard hasn't quite had that opportunity at Chelsea and that to expect him to also run around and contribute defensively in what is already a defensive set up under Jose and Conte is abit much. For Belgium he hasn't really pulled any trees nor do I envisage him doing so.. something is abit off about that entire set up, whereas the Chileans take genuine pride in turning out for their nation and are extra motivated.
Bottom line is I have an issue with people looking at comparing players as a binary concept all the time.. whereas in some situations a more nuanced approach is needed. At this moment in time, if both players were to say suffer a career threatening injury tomorrow and retire and Sanchez had just signed for City, who would be remembered as having been the better player or contributed more to the game at the highest level.
For me winning the EPL twice and being at the forefront of those sides, trumps winning the Copa America. If there was a coefficient for rating these triumphs, I'd rate winning the english league higher. That said, Hazard has had the benefit (although one could argue by being the better player thus far) of having a top side built around him whereas someone like Sanchez was a side dish at Barca (though anyone competing with Messi would be) and only managed to secure a move to Arsenal in his prime.. if Hazard was moving, Arsenal would have been blown out of the water.
Now however, Sanchez has a golden opportunity to kick on and show everyone he is on the same level as a Hazard. Hell, he could prove he's even better and that is the thing. The opinion Hazard is better isn't fixed in stone, Sanchez has brilliant work rate, better goalscorer and superior mentality I would argue.. sort of guy who fights when the chips are down. So there is no reason why in a couple of seasons, the situation can't be reversed. However right here right now.. for me Hazard has done more in his career to be remembered as the better player.
Look at recent games v Chelsea, and tell me you weren't more fearful of facing Hazard then we have been when facing Sanchez.