You’re probably wondering what skeuomorphism is. Don’t worry if you’re not sure, because you’ve definitely seen it.
Skeuomorphism describes the way a design borrows a particular feature from the past, even when the need for it has gone. For example using a monophonic ringtone on a brand new iPhone, when you can use actual audio. A flat design is self-explanatory, embracing visual minimalism using simple shapes and colours.
A skeumorphic design will look much more realistic to the eye, due to the way colours and shapes are used. Flat design has come into play recently, due to the love of nostalgia. If you look at smartphone games, you’ll see that flat design games seem to be more popular. Whilst this may not be just down to the design, it definitely plays a part.
Overall it depends on what you’re designing. So test out both styles and see what works well.