MDF can definitely be a mixed bag, most "builder-grade" or "readily available" MDF is definitely cheaply produced and prone to fraying.
There are better quality ones are are moisture resistant, and some that hold up really well to cutting, like Medex, tho it tends to be more expensive.
That said there are definitely good reasons to go with BB plywood, esp the higher quality "marine grade" multi-ply versions, and wont have the issues with fine dust and fryaing like most forms of MDF.
The biggest struggle with Plywood is always the edges/corners which need to be well filled and sanded for clean results, where MDF only need to be cut then sealed with minimal sanding.
But I also know there are people on here that refuse to work with MDF & can still produce an excellent product, & others who dont mind either way.
It's really down to where your preference/skills lie.