Are there benefits to developing an application on two or more different platforms? Does using a different compiler on even the same platform have benefits?
Yes, especially if you plan to distribute your code for multiple platforms.
But even if you don't cross platform development is a form of futureproofing; if it runs on multiple (diverse) platforms today, it's more likely to run on future platforms than something that was tuned, tweeked, and specialized to work on a version 7.8.3 clean install of vendor X's Q-series boxes (patch level 1452) and nothing else.
There seems to be a benefit in finding and simply preventing bugs with a different compiler and a different OS. Different CPUs can pin down endian issues early. There is the pain at the GUI level if you want to stay native at that level.
Short answer: Yes.
Short of cloning a disk, it is almost impossible to make two systems exactly alike, so you are going to end up running on "different platforms" whether you meant to or not. By specifically confronting and solving the "what if system A doesn't do things like B?" problem head on you are much more likely to find those key assumptions your code makes.
That said, I would say you should get a good chunk of your base code working on system A, and then take a day (or a week or ...) and get it running on system B. It can be very educational.
My education came back in the 80's when I ported a source level C debugger to over 100 flavors of U*NX. Gack!
Some platforms have really dreadful development tools. I once worked in an IB where rather than use Sun's ghastly toolset, peole developed code in VC++ and then ported to Solaris.
Are there benefits to developing an application on two or more different platforms?
If this is production software, the obvious reason is the lure of a larger client base. Your product's appeal is magnified the moment the client hears that you support multiple platforms. Remember, most enterprises do not use a single OS or even a single version of the OS. It is fairly typical to find a section using Windows, another Mac and a smaller version some flavor of Linux.
It is also seen that customizing a product for a single platform is often far more tedious than to have it run on multi-platform. The law of diminishing returns kicks in even before you know.
Of course, all of this makes little sense, if you are doing customization work for an existing product for the client's proprietary hardware. But even then, keep an eye out for the entire range of hardware your client has in his repertoire -- you never know when he might ask for it.
Does using a different compiler on even the same platform have benefits?
Yes, again. Different compilers implement different extensions. See to it that you are not dependent on a particular version of a particular compiler.
Further, there may be a bug or two in the compiler itself. Using multiple compilers helps sort these out.
I have further seen bits of a (cross-platform) product using two different compilers -- one was to used in those modules where floating point manipulation required a very high level of accuracy. (Been a while I've heard anyone else do that, but ...)
I've ported a large C++ program, originally Win32, to Linux. It wasn't very difficult. Mostly dealing with compiler incompatibilities, because the MS C++ compiler at the time was non-compliant in various ways. I expect that problem has mostly gone now (until C++0x features start gradually appearing). Also writing a simple platform abstraction library to centralize the platform-specific code in one place. It depends to what extent you are dependent on services from the OS that would be hard to mimic on a new platform.
You don't have to build portability in from the ground up. That's why "porting" is often described as an activity you can perform in one shot after an initial release on your most important platform. You don't have to do it continuously from the very start. Purely for economic reasons, if you can avoid doing work that may never pay off, obviously you should. The cost of porting later on, when really necessary, turns out to be not that bad.
Mostly, there is an existing platform where the application is written for (individual software). But you adress more developers (both platforms), if you decide to provide an independent language.
Also products (standard software) for SMEs can be sold better if they run on different platforms! You can gain access to both markets, WIN&LINUX! (and MacOSx and so on...)
Big companies mostly buy hardware which is supported/certified by the product vendor only to deploy the specified product.
If you develop on multiple platforms at the same time you get the advantage of being able to use different tools. For example I once had a memory overwrite (I still swear I didn't need the +1 for the null byte!) that cause "free" to crash. I brought the code up to speed on Windows and found the overwrite in about 1 minute with Rational Purify... it had taken me a week under Linux of chasing it (valgrind might have found it... but I didn't know about it at the time).
Different compilers on the same or different platforms is, to me, a must as each compiler will report different things, and sometimes the report from one compiler about an error will be gibberish but the other compiler makes it very clear.
Using things like multiple databases while developing means you are much less likely to tie yourself to a particular database which means you can swap out the database if there is a reason to do so. If you want to integrate something that uses Oracle into a existing infrastructure that uses SQL Server for example it can really suck - much better if the Oracle or SQL Server pieces can be moved to the other system (I know of some places that have 3 different databases for their financial systems... ick).
In general, always developing for two or three things means that the odds of you finding mistakes is better, and the odds of the system being more flexible is better.
On the other hand all of that can take time and effort that, at the immediate time, is seen as an unneeded expense.