I apologize for the late respond. I had work as well.
There's a lot of different ways to determine how Teddy Long is the better on-screen general manager, and I'll show you just why he is.
Teddy Long is the longest employed general manager in WWE history
Teddy has been a general manager in WWE (ECW as well as SmackDown) for over 5 years. That is much more than Eric Bischoff can brag about. It shows that in an on-screen perspective, there's more reliability and experience from Teddy Long's part.
Teddy has only been on probation, and I believe he passed that one as well. What happened to Eric Bischoff's period in WWE? Oh yeah, he got his ass fired.
Eric Bischoff, as opposed to Teddy Long is a guy that doesn't take shit from anybody, and who had problems with Vince McMahon at times. Teddy Long is a loyal employee who obeys the word of his boss. From that perspective in a kayfabe on-screen way, Teddy Long is the better general manager.
Teddy Long upholds the rules, he's a face, he doesn't bend them.
While the general manager is an on-screen authority figure and practically his word goes. There's still certain rules to go by in general, something that Vince McMahon as boss relies on to be uphold. Teddy Long's first night had him fining Kurt Angle for not having his wrestling gear available, therefore, upholding the rules.
Eric Bischoff has on numerous occasions bended the rules for his own, as well as his allies (namely Chris Jericho in 2005, the match where he got fired). Eric Bischoff has done this on numerous occasions, both in WCW and WWE.
Teddy Long has never tried to run his company out of business.
Remember nWo? Yeah Eric Bischoff was a part of the New World Order. If you have no idea what the New World Order is, it's one of the biggest factions ever in the business, and from an on-screen perspective they tried to run WCW as their own show.
Teddy Long on the other hand, has remained once again, loyal to Vince McMahon, and has in no way or another tried to ruin the company that employs him. Teddy Long is therefore more trustworthy as a general manager as well. Better said, Teddy Long doesn't butt-fuck you (to put it a bit harshly).
Teddy Long is giving, yet fair.
Remember the tournament to crown the United States champion back in 2005? When he stripped Booker T of the United States championship. Something which I believe launched for a battle royal to allow talents to gain the illustrious championship (I could be wrong, irrelevant to this thread nonetheless).
Teddy has reversed a few decisions here and there where the champion, or the challenger is unfairly put in a position where he looses the championship match. Just as well as he is fair to give a championship rematch where things like this passes through. Teddy has also balanced wrong and right on a few occasions like CM Punk's submission victory over The Undertaker, a.k.a the second screwjob.
Teddy Long is just overall more entertaining to watch
Now this is all an opinion. However a lot of this debate is gonna be opinion, because we need to convince the judges.
Anyway, Teddy Long is definitely much more entertaining than Eric. Sure Eric is a great heel, but Teddy Long is just an overall great face as well. Teddy Long gets a decent pop every now and then, he works a bit of his Ebonics slang into his language, which makes for him to be an overall more entertaining character to watch.