Well to be fair, that's only when it comes to long drawn out bits of conversation between the characters. WHenever someone learns a lesson, sets up a cutaway, or has a plot relevent conversation, the dialogue is incredibley forced and weak. Especially in the later seasons. Literally, if you sit down and analyze it, sometimes how they get from joke to joke is by just spewing bullcrap to get from one part of the conversation to the rest. Or just a bunch of generic tripe. This is obviously an exception since like I said the actual conversation is good, but let's face it: actual conversation in a usual ep is what 30% at most.
IMHO Peter's the easiest character to write for, and the easiest to involve in pretty much any story, but he has very very limited depth. Stewie and Brian over time have developed actual consistent personalities and have limitations on they're personalities you don't realy have as much with Peter. Peter is really more of the go to guy for the comedic backbone or for some random activity but that's really it. Unlike say Cartman of South Park who is both the show's most humorous yet at the same time most interesting character, Peter is just supposedly the funniest, as even Homer is a lot more complex by nature.
Then again I don't think even a simpsons relationship has actually gotten as overly complex as Stewie and Brian's. As someone pointed out this episode wouldn't of worked if the two didn't have they're long history behind them. Because it actually not only builds on that, but is actually why we feel something for them at the end. To me, anytime Peter said he loved Lois or that he learned some supposed lesson it felt empty and flat, like there was a problem there that needed solving and they just did it to be convientant. However when Brian admitts to thinking sometimes he'd end it all and not feeling his dog like instinct, that actually not only felt real, but something not just forced. As it was something in the background and it was identifable. And by that notion Stewie opening up felt more human as well because it didn't totally fix the problem. Brian still has his issues but now just feels better knowing Stewie does really care for him like that (and it naturally came out in some rather good lines, like Stewie admitting he only hurt Brian since Brian hurt him, or that he didn't just like Brian in a homosexual way). I guess the poop eating in the opening had a point but it did feel stretched out rather long, but I guess that's just the kind of humor they like. Having the end though be a character study shows a maturity FG actually has that isn't just shallow or something to pad time between all the jokes. THough really it can only be done with characters with 3D Personalities like Brian or Stewie. Locking anyone else in the safe for an hour just wouldn't of worked.