I can only answer this from a perspective of using the SQL Server BI stack but I thought I'd share some thoughts.
I'm going to assume a scenario of data warehousing whereby you would have your various sources being pulled into a staging database and then onto a DW......
I have had experience of using SSIS to talk to Oracle, flat files, TeraData and web services and pull data. The key is getting the correct drivers for your needs.
From there the data would be pulled into the SSIS buffer effectively making the experience from that point on the same as with native (SQL Server) data.
There are other things to consider here like cross network speed/reliability vs how much data you are extracting on a day to day basis.
Once you have your DW built then you can look at things like SSRS and SSAS. I am biased as I love SSAS! The one thing I would say of the entire process is that it takes a lot of careful planning and if you do go down the DW route then be sure to read up on the different methodologies and select one that suits.
Good luck :-)
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