There's even more to this. davnicwil says just use the same sponge cake and excel in your area of expertise: the icing. Good advice.
Alternatively, if you are a "fast follower": after the other company has evangelized the new feature (sponge cake) and started to build an audience for it, you can see what features seem to really matter and either make a simplified one or one that addresses the limitations of it.
A great example is the iPod, the famously lame latecomer ("no wifi, less space than a nomad. Lame"). Apple launched into a market which was already developing (tiny MP3 players), and not only put their own "icing" on it (e.g. design) but addressed a couple of the fundamental problems with the existing ones (the complexity of getting music into them and navigating to find what you want). So they weren't even really competing with the other players.
Agree, and to dive in a bit more to the icing, one of the most important and least remembered ingredients in that icing was the 1.8" Toshiba hard drive. That allowed for the miniaturization of the iPod relative to other, clunkier players like the Nomad that used much larger 2.5" laptop hard drives [1], or flash-based players that could store only 25-50 songs.
Combined with iTunes, they solved for the end-to-end experience: easy to use, easy to carry around, easy to manage your library. Other players only solved for the narrow experience of playing music.
To be honest, though I do like the industrial design of the first iPod, it was perhaps the weakest part of the icing. The click wheel hadn't even been invented. It was all about the three pillars of iTunes, compact size, and '1000 songs in your pocket'. Despite the subject of the post being about copying, on iPod they actually copied very little from existing products of the time, in style and substance.
iPod is a wonderful example, and Apple in general too - They stole the idea of what devices to build (existing categories), copied the tactics and methods of actually building them (commodity parts) but extended the ideas sufficiently to not simply make yet another variant, but something truly new and much better.
Alternatively, if you are a "fast follower": after the other company has evangelized the new feature (sponge cake) and started to build an audience for it, you can see what features seem to really matter and either make a simplified one or one that addresses the limitations of it.
A great example is the iPod, the famously lame latecomer ("no wifi, less space than a nomad. Lame"). Apple launched into a market which was already developing (tiny MP3 players), and not only put their own "icing" on it (e.g. design) but addressed a couple of the fundamental problems with the existing ones (the complexity of getting music into them and navigating to find what you want). So they weren't even really competing with the other players.