I would chime in that what can be made with those different softwares is indeed very different in sound. My main preference (despite the fact I suck at getting the best out of it) is LSDJ on the DMG. I have also produced an album a couple years ago using an iPhone and Nanoloop, it's really a good tool in that platform. I bought Nanoloop 1 & 2 at the same time a couple years ago but haven't done much with them because I don't like them on the Gameboy, and believe me they work and sound completely different when using it on Gameboys rather than a mobile device.
To start with, LSDJ is far more precise and perhaps "authentic" (a debatable point) than Nanoloop in terms of how you are working with the Gameboy's hardware. The power of sound design, the real depth of it all is top notch with LSDJ, especially thanks to its capability to apply tables. All in all though, strictly speaking on the original Gameboy, I don't know that I've ever heard anything that couldn't be equally produced from LSDJ vs Nanoloop, so in that particular case it may really come down to preference of working environment. I may in fact be wrong but I've only got my own exposure to go on. Perhaps some our Nanoloop loving peeps could expound on this.
Now, the GBA is a different beast if you look at Nanoloop 2. That hardware is capable of producing sounds that the original Gameboy cannot and Nanoloop 2 is designed to take advantage of all that. Check out music from a bloke named "Cheapshot", he has a fantastic range of GBA based stuff that can easily demonstrate the diffrence of the GBA from the DMG.
For the record, using LSDJ on a GBA makes no difference, it will only produce the sounds that it was designed for, which is the original Gameboy.
Nanoloop on iOS/Android has about zero to do with Gameboy chip music. It can easily use wav sample libraries and manipulate those samples in all kinds of ways. It's synthesis is not really related to the Gameboy sound design in any way. That said, it is capable of some chippy sounding stuff, or the opposite and it can do a far more conventional approach to electronic music of any style.
There is of course the new Nanoloop Mono for the DMG that I have not been exposed to save for a couple of Youtube vids, and that shiz seems to be an entirely new beast, makes some pretty gorgeous sounds.
So to answer your main question, they are indeed different tools but they don't all necessarily produce the same output, they've all got their advantages and disadvantages when compared to one another. In terms of style of musIc, that's all on you. It really comes down to understanding the actual sounds/instruments you can create in these different environments and choosing what you like best. I don't think it would be fair to say (just as an example) that LSDJ is supreme for creating one style of music over Nanoloop, or saying the GBA is supreme to the DMG because it can produce different sounds. So again, once you understand what different things you can get from these softwares, you can produce any style you want to.
Good luck mate.
