Re: the frame differences:
The 3 frame startup diff may seem small, but it makes a noticeable impact when you're, say, kicking OOS or trading in the air. Bair comes out on frame 5 vs. frame 8, so that could be the difference between beating your opponent's move or taking damage. Also, combined with its shorter endlag, you can do things with bair that you can't do with fair -- an example is BJN's mention of double bair'ing in a short hop, particularly useful vs fatties.
As far as safety goes, they're both pretty committed moves, so I won't pretend that bair's shorter endlag makes it safer to use.... but it is marginally less laggy.
Baby terms ~ Bair is faster, and because it's less laggy, you can do things with it that you can't with fair.
Re: the Sakurai angle:
First of all, I'm not sure why linking to an accurate source about the Sakurai angle is funny? Or why it's bad that it's a "new gen term" considering it affects trip percentages, so it's become more relevant in Brawl. Anyway. I just tried to find a site that would explain it as simply as possible..... it's hard to clarify if you're not knowledgeable about Brawl mechanics though.
Basically, a move with the Sakurai angle is marked as having a 361 degree knockback (kb) angle but actually has variable knockback depending on whether the target is grounded vs. aerial and how much damage they have. So as they approach KO percentages, the move's kb angle will change (only on grounded opponents -- on aerial opponents, it's always 45 degrees).
Baby terms ~ There are none. You either understand this or don't, honestly. x.x
Re: the knockback difference in general:
I'm not 100% sure whether I'm right in bair having the Sakurai angle or BJN's right on the kb numbers he posted earlier (like I said, I haven't done Smash Lab research or looked at Zelda's move data in ~2 years, so he's probably right tbh), but whichever is right, bair has better knockback at high percentages. It has higher kb strength in terms of base kb and kb growth (how much the kb strength increases as the target's damage increases); additionally, if it does have the Sakurai angle, it will send grounded high damage opponents at an angle less than 45 degrees, which sends them on a trajectory with less distance to the blast zone. (Obviously DI plays a huge factor in angles, but 45 degrees is generally the worst angle since with no DI it sends people straight to the upper corners.)
Baby terms ~ Assuming no difference in DI, bair kills sooner than fair because it has better knockback values.
Otherwise, they're pretty much the same. Bair isn't wildly better than fair, but it's better enough that it more or less makes fair obsolete except for damage building or if you're facing the wrong way when you have an opportunity to kill.
Baby term conclusion ~ Everything fair does, bair just does better. And does a few minor tricks fair can't.
Okay, I think I'm done editing for clarity. ;; If it's still not simple enough.... I dunno what to tell you!