Which paid summoning banner is better?

Overall the Calvary banner is stated to be better, but there is still a chance for some bad servants like medb and such, but still no 5 star is not worth it. Don't go in hoping for a certain class or servant.

This may be the most generic answer you might get, but really, it depends on what you need the most. The available archers are Orion (anti-Male ST), Tesla (anti-Heaven/Earth AoE with a NP charge button), and Arjuna (somewhat lackluster AoE with instant death for divine servants). Casters, on the other hand, are Waver (no need to say anything), Tamamo (best arts support), and Sanzang (best offensive Caster ST). My personal opinion says you should try for a Caster, since there are good Archers for a smaller cost.

Either banner has some good stuff, but Cav banner is generally considered to be better, because the absolute worst servant you could pull is Medb, who really isn't as bad as some people like to say.

Knight banner has more "duds" if you want to call them that, but just about any five star you pull will be worth investing into

In my honest opinion, there is little reason to roll the 3 knights banner over the horsemen banner unless you just like the servants in that one more. Just looking at the lineup, most of the servants in the horsemen banner are just more useful for more situations.

The best things in the knights banner are arguably:
- Jeanne, who won't be amazing until much later when her NP is strengthened
- Karna, one of the few 5* AOE lancers.
- Altera, one of the better 5* AOE sabers.
- Tesla, a good AOE archer, but lackluster compared to Gilgamesh
- Altria (Lancer), another AOE lancer.

Compared to
- Cu Alter, best berserker in the game
- Tamamo, best arts support in the game
- Jack, best star generator in the game and excellent last man standing
- Ozy, best rider in the game
- Waver: best general support in the game
- Xuanzang: best offensive caster in the game

There isn't really much contest. Also, most of the best from the kinghts banner are AOE, whereas most from the horsemen banner are ST.

BTW this answer is a bit simplistic and doesn't really take into account what you need, but honestly when one banner has some of the best servants from their respective classes and the other doesn't, its probably more worth it to roll thee former.