Here's my thoughts as someone who loves the original and has tried with BB2K (I will admit that I think the MUSIC in BB2K is almost as good).
A) John Belushi. Belushi was such a charismatic presence that he lights up the screen
B ) Tighter Script. As the pod points out, the plot to the OGBB, while being a series of vignettes, it followed an easy to summerize plot. Elwood picks up Jake, they go to the orphanage, get their "mission from God" to save said orphanage, put the band back together, put on a show. Everything is building up to that show. The final show feels like a show. Yes there are only two numbers, but you get the impression it would go on longer if John Candy hadn't showed up. The climax makes sense (the car chase) to pay the bill and ending up in jail. In BB2K, it is just vignettes. The plot makes no sense, why does Elwood want to go to Erkahau Badu's BotB? When the state police (and seriously at this point it would be the FBI and not Nia Pepples--or why wasn't Joe Morton and Nia Peeples just FBI agents) show up, they run but there's no climax to the run. Why do Mighty Mack and Joe stay (they would be held as accessories to the crime--ESP. Joe Morton) but Elwood and Scribbles run?
C) Inherent Logic. The OGBB, while having crazy stuff happen, has an explanation (it's a former police cruiser with a souped up engine--there's also a cut bit where the powerlines Elwood parks under have given it some abilities but that's cut so neither here nor there). The car that they use in BB2K makes no sense and has no inherent logic. It goes underwater, it has a bedroom, it just does things for no reason.
D) Why the band reforms makes sense. In the OGBB, these guys, for the most part, are living the lives of working musicians. Two work in a soul food restaurant (for Aretha Franklin-Matt Murphy's on-screen wife), some are working as lounge musicians at a holiday inn, only the trumpet player seems to have a good job (as the maître d') and reluctant to join them. In BB2K, everyone but Elwood has seemingly good jobs. Willie owns his own strip club, the Murphy's own a Mercedes-Benz dealership, the keyboard player seems to have a good job at the sex phone line as a supervisor, two are radio DJs. Their second vehicle is a Benz! it seems like for everyone, this is dad rock, it's a lark. So why would they risk getting mixed up with Elwood Blues, who according to the first movie has sent them to jail at least two previous times. Jack was the charismatic force in the first one that drove them, without Jake and Elwood these guys have seemingly got their lives together and have no reason to go back on the road.
E) MAGIC! I mean crazy stuff happens in OGBB, but nothing that is flat out magic. The closest is Jake's revelation at James Brown's church (similar to Joe Morton's but without the full Blues Brother's transformation) but that could be interpreted as a demonstration of Jake's internal revelation. in BB2K you have Joe Morton's transformation, you have Erkah Badu turning them into ZOMBIES and turning Darrell Hammond's white supremacists into mice.
That's just off the top of my head