Combined they have around 11 world titles, I
Erh, so which one of the wrestler's amount of title reigns did you just kill off?
Edge is a 9 times world champion, and Randy is a 6 times, so that would be 15 title reigns.
Anyway, I guess we have to look at a few things.
Mic wise, I find Edge superior to Randy Orton, certainly they both have the great voice for heel work, and they have own mean kind of ways to cut a promo, Randy the more calm or mediocre angry person (at least by his voice it sounds like that, certainly listening to the words, you could agree that he could seem pissed off at times during his promos like his common use of "who the hell do you think you are") where as Edge has the ability to pretty much sound angry at any given time because of the roughness in his voice, and because he has great facial features to act angry.
As you said yourself, Edge is a clean win in the hardcore wrestling section, with his storied past in TLC matches etc. where as Randy certainly can wrestle a hardcore match, Edge once again gets this win.
Title reign wise, it's quite obvious once more, Edge is the winner, having held basically everything there is to hold in WWE history except for the ECW, Hardcore and European title, and the belts that he didn't fall into category for (Cruiserweight and Lightweight championships) where as Randy has mainly held world titles, now you'd think that would make Randy superior to Edge in the title reign section because Randy has spend the most of his career in the main event picture, wrestling for the title, as opposed to Edge who took years to even gain his first world title, which brings me to my next "section"
Elevation: Yes Randy would actually be winning this one, because he was quite obviously elevated much more solidly and quicker than Edge, having the back up of two of the greatest wrestlers ever (Yes I would call Triple H one of the greatest ever, not in the top 10, but he's up there among the people that you'd look back on among the greats) in a great faction, as opposed to Edge who basically build his reputation on tag team wrestling, and doing high risk stuff that wowed people alongside Christian and the Hardy's.
Technical wise, I'm not quite sure, as we know Edge has slowed down in his abilities in the ring ever since his neck injury, and now his Achilles tendon tear, which obviously has put Edge on the hold as of late, also taking into consideration that he hasn't really wrestled any match as of late going into Wrestlemania, but that's not something that should damage the fact that Edge can put on one hell of a match, as the one with Owen Hart back in the years, his match with Christian, and most recently, the match he had Vs John Morrison briefly after loosing the World Heavyweight Championship after Extreme rules.
On the other hand, Randy Orton certainly has the ability to put on a good match himself, even successfully ranking among the few people that have performed for 1 complete hour in an Iron Man Match, which I personally think was a damn awesome match, perhaps thanks to the weapons, but that's another story.
Although Randy has some matches where he basically goes around and does a few of his routine attacks, and a few stomps, then an RKO, which ranks far away from a good technical match, and yes you could counter with "But all Edge has done as of late is spearing people" but lets remember, he's most likely still healing for Wrestlemania, Wrestlemania will be his time to show he can still go with great technical wrestlers such as Chris Jericho.
So, even though I know your love for Randy ThomasRKO, I will lean to Edge being the superior wrestler, simply because he is better all around based, he has had a solid career of many titles, amazing memorable matches, and great mic skills, which is what in my eyes makes a great wrestler, all-round stability as a performer, a wrestler and an entertainer.