Configuring euthanasia reasons will allow your organization to track more granular reasons for euthanasia whereas euthanasia subtypes are typically configured as higher level reasons. 

For example, you may have the following outcome types/subtypes:

Outcome Type: Euthanasia
Outcome Subtype: Owner Requested

Outcome Type: Euthanasia
Outcome Subtype: Medical

Outcome Type: Euthanasia
Outcome Subtype: Aggression

However, within each of those subtypes, you may want to be able to report on a more granular reason for the euthanasia outcome which is where euthanasia reasons can be really helpful: 

Outcome Type: Euthanasia
Outcome Subtype: Owner Requested
Euthanasia Reason: Geriatric with poor quality of life

Outcome Type: Euthanasia
Outcome Subtype: Medical
Euthanasia Reason: Terminal Illness

Outcome Type: Euthanasia
Outcome Subtype: Aggression
Euthanasia Reason: Aggression Towards People

Deciding to use euthanasia reasons will depend on how your team plans to report on these outcomes (euthanasia reasons are only available in the Euthanasia Details Quick Report), and whether you are comfortable using subtypes only - or if you'd like an additional level of detail captured for each outcome with a euthanasia reason.