There is a lot to say on what makes the Fate/Zero anime work so well compared to other Fate series.

For one, it has probably the most managable cast-size of any series adapted, 7 Masters, 7 Servants and a few supporting characters. This keeps it from feeling overwhelming with too many characters like Apocrphya or underwhelming like watching any one route of Stay Night alone.

Additionally, in comparision to characters like Shirou from Fate/Stay Night, most Fate/Zero characters are observed from a neutral outside perspective, meaning that the issues that happen adapting something exclusively featured in internal monologue don't rear their ugly head. Especially when this might include key details of motivation or character development. Most characters in Zero will either say it themselves or be observed and remarked upon by another so the audience can clearly see those things spoken out loud.

This also combines with how Zero has three main focus characters in the form of Kiritsugu, Kirei and Waver (at least in my interpretation) whose growth is a key focus of the series as opposed to just one like Shirou or Sieg. The lack of absolute focus means that they have to be more explicit with their development to make up for said lack of focus. (It also helps that the anime changes Kayneth from just rejecting Waver's thesis to publicly humiliating him to make Waver's actions fell more justified.)

There is also something to be said in how Zero has alot of set-pieces that can be adapted into cool action scenes. Whilst all series have them, Zero's has the tightest and fasted pace of any series, leading to visual specticle following visual specitcle. (spell check that).Compare this to the slower pace of the various routes of Fate/Stay Night with their