We are currently looking at moving from Spotfire to Tableau or Power BI. Our data is complex oil and gas data, not large volume retail or bank data. Any thoughts or experiences with this?

Data needs to be curated into manageable, focus dataset or data mart, then have visualization tool to access for the given purpose.  Personally, Tableau. 

What do you need the tool to do?  Power BI and Tableau are both visualisation tools and will work better if you have other data processing behind them to build easy to use and understand data sets.  

If you have your data in a Microsoft ecosystem, then PowerBI is probably a no brainer.  Otherwise, personally, I think Tableau is easier to use and easier for non-technical people to play with over data sets that you have prepared.

Depends on what you want the tool to do. Each has a strength but neither is well known for large data or heavy transformation work.  Better off looking elsewhere for those needs.