The only time the the WWWF/WWF/WWE Championship could be considered THE most prestigious World Title was from January 1999 through August 2002 when it was the only title that could claim to being a "World" Championship that actually meant anything.
Are you talking about the same title where the owner of the promotion, Vince McMahon, put the belt on himself? Yeah Hogan winning with a fingerpoke was horrible but hilarious and rumor had it that this was to setup Goldberg's rallying back to the World Title (I can't confirm this as being the truth but I heard Nash mention it once, he could be lying, but he'd have a better idea about this than you or I), you justified the Ted DiBiase purchase of the WWF Title by saying there were "reasons" he did it, which is true, he was the Million Dollar Man he wanted to take a shortcut to the World Title and he did that. Well Hulk Hogan was the tyrant of WCW when he formed the nWo with Hall and Nash, he made a plan with Nash to bring the nWo back together, hence the idea of the Fingerpoke of Doom. So yeah for as tacky as that might have seemed, there was a justification for how Hogan "won" the belt from Nash.
Now I don't deny that David Arquette and Vince Russo's title wins were farcical (Those title reigns were far more damaging than anything Hogan could have done) but the hot potatoing of the WWF World Title was just plain ridiculous during that time. Thankfully, the WWF Attitude Era had more than just the WWF Title to rely on during that time or else things would have gotten boring, very fast in my opinion.
And also not to be an anal retentive douche, but during the period you were describing the rise of Triple H, the feud between Rock and Mankind, Taker selling his soul and Austin being Austin, it was called the WWF. In my opinion, referring to that company as the WWE in the context of anything pre-May 6, 2002 is an insult to its history. Oh and about Shawn Michaels and Triple H's WWF European Title match, you're right the European Title didn't matter, but that was a farce as well, the European Title never should have existed in the first place.
Anyway my vote for the most prestigious time for the WWE Championship is when it was still the WWF World Heavyweight Championship, and this was when Hulk Hogan first won it, while I was and still am a fan of Hulk Hogan's other reigns. It was his first one that mattered the most, just because he was constantly wrestling from 1984-1988 (but we can even add his second one in 1989-1990 was an honorable mention too) and his variety of opponents was just amazing. I mean Hogan ran the gamut, yes some wrestlers were better than others but Hogan had one of the longest lists of challengers and yes there were many that were in very similar molds but at the same time, people came to watch it and it worked. Granted I loved guys like The Rock and Austin, but by comparison the variety just wasn't there in my view. Anyway, let me continue...
Greg Valentine
Don Muraco
Brutus Beefcake
"Ravishing" Rick Rude
Adrian Adonis
"Macho Man" Randy Savage
"Dr. D" David Schultz
Iron Sheik
Nikolai Volkoff
"Cowboy" Bob Orton
Killer Khan
"Mr. Wonderful" Paul Orndorff
Big John Studd
Roddy Piper
Kamala
One Man Gang
Ted DiBiase
Andre The Giant
King Kong Bundy
Terry Funk
Harley Race
Jake "The Snake" Roberts
And then of course if we look at Hogan's second reign, he had a few more opponents to add to that list of the gamut of challengers.
Mr. Perfect
Honky Tonk Man
Big Boss Man
The Ultimate Warrior
As we all know the only man in that list during the "Hulkamania" era to beat Hogan cleanly was The Ultimate Warrior, but during that time that Hogan had those first two WWF Title reigns, I felt the title was most prestigious, despite the same guy retaining everytime, the whole idea of who Hogan was going to take on next was just plain intriguing to me, and as you can see millions of others or else Hogan never would have been the champion for as long as he had been.
It's sad that wrestling can't have that same dynamic anymore.
But for an honorable mention I do want to bring up Bret Hart's WWF Title reigns as well...during a time that the WWF needed a new face to carry a title division that was lacking star power, Bret Hart stepped up to the plate and had great matches. Bret's 1992 Survivor Series title defense, his first PPV title defense which happened to be against Shawn Michaels is an overlooked match that never gets the same regard that the Iron Man Match and Screwjob do, for obvious reasons, its storyline importance is not as significant but man that was a wild match, I loved it. I also enjoyed Bret's matches against Diesel, Bob Backlund, Razor Ramon, Yokozuna and to be honest I think my favorite Bret Hart WWF Title match was the Steel Cage match with Owen Hart at SummerSlam 1994.
Just my two cents though.