For example, Pentel leads run a bit harder than other Japanese brands. This makes them a bit more brittle. For a 0.3 mm pencil without a sliding sleeve to support the extended lead, I would choose a Pilot or Mitsubishi lead to reduce breakage.
Sometimes you want to make really bold and dark lines, so you go for a 0.7 or 0.9 mm with the darkest lead you can find. Those sizes are only made as soft as 2B, but the Pilot Neox Graphite 0.7 & 0.9 mm 2B is actually more like a 4B. It's the darkest lead currently on the market in those sizes. (I have some long-discontinued 6B that I use sparingly.)
When I'm writing on index cards, I usually want a harder than usual lead, writing with a sharp edge to make clean lines that won't smudge. I like Faber-Castell HB in 0.9 mm for this because their harder leads don't feel as gritty as other brands.
I have a variety of other graphite leads that I use for specific situations.
Getting into color, for its variety of hues, the Mitsubishi Uni Nano Dia Color in 0.7 mm is usually my first choice. It makes bolder lines than the same brand in 0.5 mm, because the greater thickness allows a lower percentage of structural polymer in the mix.
A big problem with the Nano Dia, though, is that it's not lightfast. Most of the colors will fade away after a month on the bulletin board. The most lightfast colored lead is the Staedtler 0.5 mm in red/green/blue. It is extremely brittle, though, so you need to use it with a sliding-sleeve pencil like the Pentel Orenz. (https://www.jetpens.com/Pentel-Orenz-Mechanical-Pencil-0.5-m...)
Aside from situation, people have different preferences in how the tip feels on the paper. Pentel feels rather slick, Pilot has a more chalky feel, and Mitsubishi to me feels rather gritty. I like a chalky feel when writing on really smooth paper and doing math, but the slicker Pentel suits me better when writing longhand on cheap office paper.
