Ronin94

My apologies for taking so long to respond to your question — real life snuck up on me and got in a Surprise attacking, Knocking me Out for several Segments until I could recover.
 
You make the EGO Roll for each Psychological Complication, as discussed in the rules for the Complication. Essentially it's an EGO Roll Versus EGO Roll Contest; the Complication that succeeds by the most wins. If they tie, keep rolling until one wins.
 
Alternately, forget about the dice and just let the player decide. That may lead to more fun in the campaign later, as he has to justify his decision both to himself and to his comrades.

If a character has 2 psychological complications in conflict with each other and all else is equal what do you do? For example if if a character has the psychological complication: racist and the psychological complication: protective of innocents those two complications can overlap quite easily such as if someone of the disliked race is traped in a fire but has done nothing wrong. I assume that if the complications are uneven the more severe one wins out but what happens if they are equal? Do they just cancel each other out? Thanks in advance.

For that sort of agenda, I'd suggest this older Champions "Campaign Book" which includes three short introductory adventures, which can be run singly or linked sequentially (titles on the cover):
3rd Edition Champions differs from 6E, but is not that hard to adapt. More importantly, the adventures are easy to run, and include maps.

One of the best things about all incarnations of HERO /Champions is near-total backwards compatibility.   
 
And yes, there were a number of thin adventures and larger, multi-session adventures from 4e....   ... and possibly some third party stuff for 5e?  I don't recall for certain. 
 
I have no idea what exists adventure-wise for 6e, but a quick look through the site store will probably clue you in.
 
The only caution I can give you if you're looking at older adventures is that the builds were simpler in older edtions: you may want to tweak any characters in these books by adding defenses or modifiers that didn't exist then. 
 
Or you may not want to do that; I don't know.  I will caution you, though, that if you are looking specifically for adventure modules, stay away from Escape From Stronghold.  While it's an interesting look at a "Super Jail," and has a couple of scenario suggestions, it is _not_ an adventure, no matter what it says on the cover.   
 
 
 
 

As I see it, D&D has the following advantages:
 
Name recognition.  D&D has by far the most name recognition out of any RPG and is, still, in 2019 A.D. synonymous with paper and pencil roleplaying.  In the marketing progression of repetition -> association -> trust, D&D is farthest along and is therefore most likely to be tried.  I doubt most normals could even name a second RPG. Production values.  Even the worst D&D publications have had high quality writing and graphic design throughout.  Support.  There is no shortage of modules, expansions, settings, and sourcebooks available for D&D. Low barrier to entry.  D&D is easy to start playing.  Here is your character sheet and a d20, which goblin do you hit?  Having played 5e D&D, I can say that it is not, in fact, much simpler than Hero once you get into it.  Reactions, actions, saves, spell slots, specials, armor class, paths, XP, it's dizzying.  And 5e is simplified!  But it's easy to start in a way that Hero's highly customizable character creation process is not.  (Don't even get me started on Pathfinder.  That s--t is unplayable.) Player base.  Related to all of the above, D&D has the critical mass of users that makes it easier to find a good group to play with.  RPGs are not a solo game, after all. Hero loses on every single point.
 
I've argued this before, but my approach to popularizing Hero would go like this.  (It's going to be expensive.)
 
License Marvel comics characters.  It's mind boggling to me that there is no Marvel superhero RPG that's giving D&D a run for its money.  Take a property that is enjoying unbelievable popularity right now and pair it with the one game system that can handle it. Quality.  We have to invest in copywriting, art, layout, and design.  Publication standards in 2019 are just way ahead of any Hero publication in the past two decades. Hide the system.  Hero is an RPG system and an RPG-system-creation-system, and the latter is what scares people.  List powers as "Optic Blast Level 12", not "12d6 Energy Blast No Spread 0 END Not vs. Ruby (-1/4)".  95% of the time all you need to know is you roll 12d6 for damage. Simplify.  I love the SPD chart, but save it for the "Advanced" game.  Likewise with the other figured stats (but keep Stunning).  Ditch most Advantages and Limitations.  Don't publish Entangle with half a dozen specific advantages, publish three Spider-Man web powers: Entangle, TK, and ranged Blast. Make it into a board or card game.  I wasn't kidding about simplification.  Distill Hero into a board game or card game that any kid can pick up.  Save the full power of the Hero system for "Advanced" expansions that are advertised at the end of the rulebook ("Pick up the Advanced game and make your own superhero!!") Support.  Publish some modules FFS.  Codevelop an online version of the simple and advanced games to make it easier to pick up players.  I can play Catan online.  Hero?  Nope.  
Anyway that's my approach.  I'm aware that it would require a level of resources that the Hero System has basically never enjoyed and that it's a pipe dream for this reason.  Does anyone have any embellishments?