Even though they share the same origin both styles have different techniques. So this is the difference in balayage vs ombré ;
These styles consist of beach and peroxide. unless you have virgin hair (Hair that has never been exposed to chemicals. Not even those hair colour boxes you buy from a super market.)
Both looks have a that summer look, and are suppose to look naturally blended with the roots.
In order to style an ombré the client will have her mid-length to ends bleached. And one can experiment with various colours, therefore, blue , pink, blonde, grey etc..
So there you have it, you are now clear on the whole balayage and ombré situation.
A balayage on the other hand is made using foils. Roots In this case are also left shown, but a hairstylist will be dying strands and blending with the roots ,leaving the hair in foils. This is done to separate dyed hair from the un dyed. So a balayage may have the ends slightly more darker then the mid lengths, Hence the stylist will not be dying every strand. And this will create a more natural look. A balayage is commonly done by a blonde colour.
Which one is better balayage vs ombré? To be clear both styles have a different effect although they are similar and come from same origin, this question will be answered only by a persons taste in hair.