I've worked in consulting for over half my career, with a mix of engineering, program, and product development roles.

Been in product management the other half.

In a nutshell for each.

Consulting:

+ lots of variety in terms of projects and clients
+ get to help establish direction / strategy
- wear & tear (hours / travel)
- don't own anything, usually only advising

Program Management: + best fit if you like organizing things - not the decision maker for decisions - not a creative role

Product Management: + powerful for driving outcomes + problem-solving oriented - have to expend a lot of energy navigating politics / organizations, relative to the other two