How to determine correct fixed effects in linear regression model using unbalanced paneldata
It seems that you have firm-level panel data over multiple industries in multiple countries.

Year fixed effects control for trends. Do not omit them. For others, a general rule is: ___ FE's control for time-invariant heterogeneity across different ____, but do not control for heterogeneity within the same ____. You replace ____ with "firm", "industry", "country", "industry-country", etc.

Firm FE's successfully control for all firm-level time-invariant effects that are possibly correlated with the RHS variables. So you compare different years within the same firm. In contrast, industry FE's control for time-invariant effects (that are possibly correlated with the RHS variables) across different industries, but do not control for firm-level heterogeneity (fixed effects) within the same industry. And so on. 

I personally think a model with firm FE (and year effects) is easiest to defend using. If you can explain why firms within the same industry are homogenous, you can use industry FE, etc.