I hadn't played the originals but based on the XBLA ports I absolutely disagree. But well, I don't have any nostalgic feelings towards the titles. Games have come a long way since 1998, with camera, controls, and game design improving quite a bit.
It's not a matter of nostalgia. The level design in Banjo-Kazooie is absolutely brilliant, that team of Rare's really absolutely nailed the Collectathon subgenre, knowing exactly, how to use the collectibles to ensure a great flow in the game. The levels are compact, yet free for exploration, the notes lay out the basic paths through the levels and the design ideas for each level were expertly executed.
Since 1998, there were almost no improvements in camera, controls or game design in the collecathon genre. Super Mario Sunshine in 2002 improved on the camera and the controls, but after that there was only Vexx (2003) and a remake of Super Mario 64 even released in that genre and while Vexx is a nice game, it wasn't better than Banjo in any aspect sans graphics, Super Mario 64 DS had worse controls than Banjo and the camera wasn't better either. So no, this genre was not improved on since 2002 and the improvements from 1998 to 2002 were not that notable.
EDIT: I guess I should also answer the op's question:
Super Mario 64, Zelda OoT, Zelda MM, Banjo-Kazooie and F-Zero X are still among the best games ever created, besides them, Conker, Banjo-Tooie, Rayman 2, NiGHTS into Dreams (does that count as a 3D game?) and Diddy Kong Racing (also Mario Kart 64, but MKDS, MK7 and in particular MK8 are so much better than MK64...) are great fun. For PlayStation games, there are a lot of good games that suffer a lot from the PlayStation controller not having an analog stick. The Resident Evils, Croc, to lesser extend the Crash Bandicoot games would all greatly benefit from a complete overhaul of the controls, their level design is really good though.
EDIT 2: The Spyro games also hold up particularly well, they are still as awfully bad designed Banjo-clones, that absolutely failed to capture the essence of what makes collectathons fun, as ever. They do look quite nice though.