Thanos is scared of the Hulk.
http://i118.photobucket.com/albums/o106/bigbran1/ThanosQuest1-31.jpg
Now, all Thanos says is that he has avoided this battle, or sought to avoid. It never says he's scared of Hulk; it's more along the lines of: "I'd fight him, but I'd rather not."
Now, this is also before Thanos had actually ever met Hulk as well, and before his upgrade(s). Thanos didn't know him, or know his power... he just heard the hearsay I guess on Hulk. It's incredibly hard to judge something based on that, and based on the hearsay of Hulk... a lot of people would avoid a battle with him as well.
Also, after his upgrade Thanos did something in particular that pertains to this, that he would never had done before.
What he did was journey into the Nexus of Realities. He specifically says that he would never have done this in his previous body. Which could also mean that he wouldn't have fought Hulk in his previous body as well:
http://i118.photobucket.com/albums/o106/bigbran1/ThanosQuest1-09.jpg
Plus, even if he did fear Hulk as the myth has led us to believe, it's incredibly off base for Thanos, and his history. He's fought Galactus, Beyonder, Odin, Tyrant, and beings of that nature. Of course this is after he was re-incarnated, which could mean that it might be OK in a debate against Pre-Hat Thanos, but not Thanos after he was brought back.
Also, the most visible part of this myth that the people who use this fail to see, is that he says that Champion is akin to fighting Hulk, and he would rather avoid that battle... but at the same time he went into battle with Champion. Which would be like going into battle with Hulk.
Which, on its own would rule out Thanos being scared of Hulk.
_______________
Also, of course, evidence.
These first two parts of Hulk/Thanos are from 'Infinity War'. What is relevant about this, is that Thanos was weaker in this series. He was only at about half power, or he got a power up (either one makes him weaker than he is now).
Based on after he ate his Thanos clone:
http://i118.photobucket.com/albums/o106/bigbran1/comic/WarlockInfinityWatch10-21.jpg
http://i118.photobucket.com/albums/o106/bigbran1/comic/WarlockInfinityWatch10-22.jpg
Anyway.
He insults Hulk, when he has his own back turned.
[IW]
Hulk, and Earth heroes can't break the shield...
[IW]
Thanos and Warlock do it in one shot.
[IW]
What's the first thing he does?
Go after Hulk and Thing, insulting them.
[IW]
Of course...
"Strange, leash your dog, or I will."
He is so scared of Hulk... he gets between him and Namor, and puts them both in bubbles they can't break out.
Thanos clone. And this one I believe is the one from Kazar... which would make him a low level Thanos clone.
This is quite interesting actually.
The funny thing is... that he was actually planning on giving HULK POWER.
Can't go out without this...
_______________
Now, everything about Hulk/Thanos points to Thanos having no fear of Hulk. The only way this myth can be relevant, is if Hulk was fighting Post resurrection Thanos, and even then, fear/avoiding a battle doesn't equate into you being weaker than the opponent.
This is one of the most annoying things people say, and IMO at least, this is totally busted.
Busted