Hello Varshue,
There are NO 'right' or 'wrong' ways of handling such situations. It all depends on WHAT YOUR CAREER PRIORITIES are.
Your experience so far has been into Recruitment. Many HR professionals wish to move towards Core HR/Generalist roles @ this stage of his/her career, while some like to stick to Recruitment. Each one's reasons for a decision are typically UNIQUE & can't be taken as the Bible--ONLY for guidance.
In general, for a long-term career in Recruitment, Consultancies are invariably the Best. This is because any Corporate recruitment role [irrespective of designation] essentially is limited to the needs of THAT COMPANY, whatever be the domain. While the focus in any Consultancy [the larger or more professional ones, NOT the small-time ones, like other members already mentioned] essentially HAS TO BE much larger cutting across domains/sectors, by virtue of their business model. This would enable you to add a lot of value [from the Recruitment exp point-of-view] to your resume.
However, IF your goal is to move into Core HR roles along your career path, then Consultancies are NOT the right ones for you--UNLESS the job role involves handling clients to formulate their HR Practices too [which only the large Consultancies are involved in].
All the Best.
Rgds,
TS