A common question is why there are different versions of MAME supported. Well, as most software, MAME emulation improves with time, so more arcade machine types are added in each MAME release. But, as emulation improves and get more perfect, the processor requirements to run the emulators increase as well (learn more).
So, if you have a low powered device, the 2001 version will be your best bet. It also has the advantage that the full rom set is about 2GB in size. In contrast, the 2014 version will require a powerful device like the NVIDIA ShieldTV, and the full rom set will surpass the 20GB in size.