Is there any general consensus that either Elsevier or Springer is viewed as more prestigious for publishing in engineering? What (if any) is the general consensus out there regarding publishing in  one of these journals vs the other? 

I am a mechanical engineer, specialising in fluid flow and heat transfer, so would it be better to publish my findings in a relevant Elsevier journal or equivalent Springer journal?

Is one or the other viewed by the academic community as more prestigious, or does one offer greater exposure for my work?
You need to understand that the quality of journals is not bijectively related to the company that publishes it. Elsevier and Springer are publishers, they have a portfolio of journals and are sometimes hired by professional or academic societies to provide publishing services.

The quality of the journal depends on other factors, mostly the editorial strategy which is the job of the editorial board, who are independent from the publisher. As a result, even though both the company that you listed are reputable publishers, there are large variations of quality within their respective portfolios.

The best way to know which are the good journals in your field is to ask your colleagues in particular your adviser. You can also ask the scientific librarian(s) of your institution. This is a typical task that they do. Another clue is which journals publish the good papers you read and intend to cite. If you are in the biomedical sciences, the impact factor is a useful metric, although like everything, it's not perfect.

There are also limiting factors to consider, it might be that your institution or your funding agency have requirements regarding the public archival of preprints. One example is the NIH Public Access Policy, which requires that:

"all investigators funded by NIH submit an electronic copy of their final peer-reviewed manuscripts of articles that have been accepted for publication. Submission is to take place “upon acceptance,” and the article must be made available in the PubMed Central database within one year of publication."

(All the medicine-related Elsevier journals I know about comply with this requirements, but it's best to check).