I've tried all 3 DosBox on Android extensively and have done much research on their history, and here are my thoughts:
aDosBox This is the grand-daddy of them all. It's free. But it is no longer supported. Yes, I know you get what you pay for... and in this case, you get a semi-usable DosBox. Don't expect to run too many cpu-intensive games on this one.
Pros
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* Free
Cons
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* Slow!!!!
* Based upon older 0.74 DosBox
* No advanced features such as IPX Emulation or MIDI
anDosBox This was the first usable DosBox port for Android. There was some controversy when it first came out, because the author refused to release sources (even for those who paid for it). Eventually the author relented, and started releasing source for paid customers (after a 2 week waiting period, which I'm not sure the GPL allows). This used to be many people's favorite Dos Emulator, because at the time, there was no other competition. It is reasonably fast; however, lacks many features and options of the newer DosBox Turbo. One thing I need to point out, is the author of this DosBox clone also makes a GamePad add-on called gamekeyboard (at an extra cost). He has programmed his gamekeyboard to "break" when being used on DosBox Turbo. I consider this very shady behavior. Especially, since the author originally blamed DB Turbo, when all along he designed his KB to break down.
Pros:
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* Reasonable speed
* Faster than aDosBox
* Easy to use
Cons:
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* Must pay additional $2.99 for the GamePad add-on
* Lack of options compared to DB Turbo
* Slower than DB Turbo.
* Based upon older 0.74 DosBox
* No Profile Manager.
* No MIDI
* No IPX Networking (ie. Multiplayer gaming)
DosBox Turbo This is the newest DosBox port for Android. It is, what I consider to be, the best port of DosBox for Android. Its based upon the newer SVN DosBox code, has almost every option available via Preferences, and supports the most external devices (ie. Xbox360 controller, Xperia Play, etc). Unlike anDosBox, it has a free Gamepad add-on (that I also use with OnLive!) and has a really cool Profile manager to manage all your game profiles. In my testing, the newest versions are a lot faster than even andosbox. I emailed the author about the sources, and he sent me a copy the next day with no waiting period.
Pros:
===
* Fastest Dos Emulator for Android (many times faster than aDosBox)
* 20-30% faster than anDosBox
* Free GamePad
* Profile management
* based on lastest SVN DosBox
* Keymapper
* Highly Configurable
* MIDI Sound Emulation
* IPX Networking (Multiplayer Gaming)
* Updates often
Cons:
===
* The GamePad add-on only supports Android 2.1+ devices.
Update: Benchmark Comparisons anDosbox 1.2.4 vs Dosbox Turbo 1.2.0 vs aDosBox 0.25 DosBox Turbo 1.4.2 vs aDosBox 0.25 Speedtest DOOM Timedemo benchmark comparison