So I used to think reaction options are extremely limited but with the war mage there are many ways to use your reaction and both arcane deflection and counterspell are part of subclass features and I was wondering what is the best use of reaction?

Counterspell pros: prevents AoE spells, prevents non damage effects

Counterspell cons: 3rd spell slot use, needs upcasting against higher level spells 

Arcane deflection pros: no spell slot use

Arcane deflection cons: no spells except cantrips following turn

Sheild pros: better AC bonus than arcane deflection

Sheild cons: no saving throw bonus, 1st level spell

It will depend on what is occurring. If you are against enemies that are mostly just attacking then Shield will serve you better. If up against enemy spellcasters then Counterspell is better.

If your enemies are using elemental AoEs like a dragon's breath attack then Absorb Elements is best. 

If your enemies are making you use other saving throws then Arcane Deflection is best.

It's up to you to assess that specific situation and act accordingly. They all serve different purposes for different situations. 

None are better than the other, for the same reason a hammer isn't generally better than a power drill. They're different tools for different things. 

👍

Just going to add here that an important distinction when choosing between Shield and Arcane Deflection in a given circumstance is that Arcane Deflection only applies to a single attack while Shield applies to all attacks until your next turn. Something to be aware of if you're expecting to be the target of multiple attacks.