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).
The prestige of a journal and the exposure it will offer your ideas are not determined by the publisher. Sure, some publishers are better than others on average, but differences between individual journals are overwhelmingly larger than systematic differences between publishers, so there's no way to give a remotely useful answer based solely on the publisher. It's like asking "Would I be happier living in France or Germany?" Someone must have gathered statistics on average national levels of happiness, but individual circumstances and the particular opportunities available in each country are vastly more important for answering this question. (And the issues and opportunities vary so much between people that there's no hope of compiling a comprehensive answer.)
To start on finding your own answer, you can look at the journals that publish papers you care about or consider related or comparable with yours. If more come from one publisher than the other, then that may give you an answer for your particular research topic, but again you should pay far more attention to the journal than the publisher. And why restrict your attention to Elsevier and Springer? It doesn't make sense to cut down your options dramatically until you have a pretty detailed idea of what's out there.
If you don't know what sort of papers a journal publishes (not just topic, but also importance, prestige, etc.) and can't even form an opinion by browsing, then it's probably not a sensible place for you to submit your paper. If you are just starting to publish, then you may not have a lot of opinions already, but now is a good time to start forming them. You could also ask your advisor or another mentor for advice on this topic, to get insights aimed at you specifically.
Of course there may be other considerations besides prestige and exposure. For example, some people boycott Elsevier. On the other hand, Springer is also a big commercial publisher that could be considered problematic for similar reasons.
I want to expand upon something that Anonymous Mathematician wrote: Elsevier is the subject of an ongoing boycott. As of now, 14,784 researchers have pledged to not submit, referee, and/or perform editorial work for Elsevier journals.
In my opinion the boycott is completely justified: not only are they selling our own golden eggs back to us at exorbitant prices, but they engage in shady practices such as "bundling".
Many people disagree with and don't support the boycott. But whether you agree with it or not, the fact that 14,000 researchers are refusing to deal with Elsevier bodes ill in the long term for the quality of their publications.
When you say that the journals are "equivalent" I'm assuming that they have similar impact factor/eigenscore/snip/sjr and any other metric of journal "quality" or "influence" or "popularity".
So it comes down to Elsevier versus Springer versus any other publisher. Regarding your questions:
Which would be viewed by the academic community as more "prestigious"
I don't think it matters. Prestige is usually per journal, not per publisher.
which would offer greater exposure for my work?
This also doesn't depend much on the publisher. However, I will give you some points that you might want to consider.
That said, I personally think it doesn't matter too much. The main thing that affects how well received is your paper, is the paper. If it's a good one, all the nit-picking is not that important.
Ask people you work with. See where they're publishing and ask around. What holds for one field may not hold for others. Prestige of journals is subjective and based on the opinions of a relatively small group of researchers. Asking here will get you many useless opinions, because the only opinions that matter are those of your potential readers in you field.
Also look at each journal's practices and policies to see you feel personally comfortable supporting them. It's 2014 and many people do not even look at the "journal," they simply search google for your paper. Your aim should be to increase visibility to your work and not hide it behind, e.g. needless paywalls. Choose a journal that will allow you to do this in a reasonable manner. Consider journals that let you additionally post preprints on your personal website or arxiv.
As said before, when it comes to prestige the publisher does not have much weight, the journal does.
But I have to disagree slightly with other answers when it comes to exposure: some publishers have their journals available by many more universities in the world than others, thus bringing some more exposure to the work they publish (exposure is not only availability, but availability is the first logical component of exposure). Now that large commercial publishers bundle a lot, sometimes selling all their journals to a whole country, all their journals (however obscure they sometimes are) are widely accessible. However, this does not make a big difference between Springer and Elsevier, who are both big commercial publisher with mostly convergent commercial strategies. Note that open-access journals are of course even better for availability; but the fact that SpringerLink and ScienceDirect (the platforms used to access Springer and Elsevier journals) gather so many titles under one roof makes it more likely that someone will easily find a given article (an open-access buried into the depth of the internet might be available but difficult to find).
Another difference between publishers you didn't asked for but that matters is the quality of publishing work (copy-editing, assistance to editorial boards, etc.) For an author, the work done on the articles themselves is important. If you think it doesn't matter much, then think about the difference between
A. a publisher that sends you galley proofs to be checked in one week, without any indication of what has been changed from your own manuscript (but many tiny and not-so-tiny changes having been made), and
B. a publisher that sends you an annotated version of your manuscript, showing all modifications made to it, together with the galley proof that resulted from this process, so that you can check each modification easily.
The difference is in hours of work, unless you blindly trust copy-editors. And this would not be wise. Unfortunately for you, from my experience and all the testimony I gathered about various publishers, Elsevier and Springer are pretty similar when it comes to service to the authors: they do a pretty bad job.
So in conclusion, I would say that publishers do matter to authors even when they do not want to take any political stance like the Cost of knowledge pledge. But it is hard to find a strong difference between Springer and Elsevier (if you want names of publishers that do a great job, I know a few but for mathematics).
From my recent experience and from my recent question asked here. I would say the publisher reputation matters but it also varies country to country. People from various internet communities urged me to publish in a low IF journal published by highly reputed publisher (IEEE) instead of publishing high IF journal published by less reputed publisher (MDPI). The MDPI journal is not only has higher IF but also has 4.3 Normalized EigenFactor and has citation relationship with journals like Nano Letters, Science and Nature. Upon discussing same issue with my supervisor and people from Asian communities they said go for MDPI.
I will suggest check the various indicators of journal from JCR and Scopus reports and select the journal based on its current and previous 5-10 years indicators.
