Is it worth picking up the beginner's box if you've already got the core rules? Or better to grab extra dice and one of the downloadable modules?

The modules are a bit on the weak side, I think. They are brief and not memorable.

Get the main books (shadowland, emerald empire) and dice and the novellas for the stories.

The things that make it worthwhile:

1. The Map. The 8x10 map in the corebook as a full 17x22 is really nice
2. the Palace of the Emerald Champion map. Also really nice.
3. The tokens. Nifty PC/NPC tokens
4. The adventure is well paced for new players, so-so for players with other RPG experience.
   ¤ As a "grab and go" adventure, I've seen far worse.
   ¤ It's a rewrite of the 1E corebook's adventure.

My players considered it memorable, and had great fun with it.

Note that the point totals issue is one where it's not well spelled out, but there's plenty written on that in other threads.

It also makes a key implicit exemplar: A training or testing montage is ONE scene, not many.

I don't think the adventure is amazing, but it's a nice intro for new players, and as noted the maps (Rokugan, the Palace of the Emerald Champion, and Tsuma) are all beautiful.

The token sets (which I gather they're continuing with subsequent sets) are nice to haves, too.

The mini-rulebook is nice, and I believe there are a couple of NPCs unique to the beginner box rulebook (the Kitsune, for starters).

Basically: is it a vital purchase?

No. If you're happy playing with the 'core book' rules, then I'd get Emerald Empire first, because there's a lot more material in there.

I would still recommend getting it, much like the GM's kit, though, eventually.

21 hours ago, Magnus Grendel said:

The mini-rulebook is nice, and I believe there are a couple of NPCs unique to the beginner box rulebook (the Kitsune, for starters).

Kitsune are also in Emerald Empire. p. 211. And as PC's later in the book.