In my experience, most organizations where people costs comprise the bulk of the budget address the HR Committee review first, but there are pros and cons to both approaches. 

Intuitively your existing approach makes sense, as the HR Committee is best positioned to identify potential HR policy and risk issues with a significant impact on the overall budget.  Absent other constraints, this greatly simplifies the work of the Finance Committee and provides an efficient and smooth transition to Board approval. 

At the same time, NFPs everywhere are facing increasingly tougher fiscal challenges, in particular securing and maintaining reliable sources and amounts of revenue.  So, even if the HR Committee has signed off its part, the Finance Committee may still identify significant fiscal issues (e.g., unrealistic revenue projections, additional non-HR spending priorities) which would require reworking of the entire budget and further HR Committee review and signoff of its portion.

In summary, neither process guarantees perfect efficiency every time, but both will achieve governance objectives effectively. Choosing the right meeting order for your NFP will depend on your best judgment as to where budget recycling issues are most likely to emerge first. 

Hope this helps.