"Trad RPG style" typically refers to OD&D style sandboxing. But I'm not clear if the other side is linear railroading (pre-set story) or story-creation game (story created in play by group on a meta level). Even within the 'trad' side some people think of it as about full sandboxing in an open world, some people (eg most on Dragonsfoot, IME) think of it in terms of running a series of site-based adventures like the mostly Tournament-based ones TSR published from the late '70s on. That's at least 4 distinct types of play to me, and they all have potential strengths & weaknesses.
1. Full Status Quo Sandbox - Players say "What do we do?" GM says "You're too short for this ride" or "Oops yer dead". Great for immersion though. With a bit of starting GM direction this is my favourite style these days, but can take more GM work than the other approaches.
2. Site based Adventure String - lack of feeling there's a world beyond the adventure. But decent for immersion & clearly something to do. Clear 'game' challenge.
3. Linear Railroad, scripted scenes - near-complete lack of player agency. Decent for immersion, plus players typically get to 'experience' a story much like with passive media or linear computer games - the prewritten story can be a lot more detailed & dramatic than in site-based play.
4. Storygame - Discards immersion as a goal - "not really an RPG". Agency shifts from PC to player. Can create stories that are a lot of fun in the moment, though probably make less sense than the prewritten linear type - in fact they likely make less sense than the stories that emerge naturally from pure sandbox play.