Hey Auntjemimma,
I don’t know if I am the right person to be asked this, since I hate both. Since I am someone who learned to build things with solid/natural wood (lumber), I don’t like engineered wood which means that the wood of the trees that I love are chopped into pieces before even using them.
I don’t see advantages of melamine over MDF in this application. Melamine is toxic both in production and in processing, I can live without melamine.
Most people here would say you’re good with MDF for the wasteboard and most will use it for table top too. Its advantage is that because it is engineered material, it is reliably flat, although it is not stiffy at all and will twist if the support to which you attach it to is twisted.
If you ask me personally, I plan to use a wasteboard made of HDPE, there was one shown in the forum the other day. Otherwise I use solid wood (natural wood, lumber), e.g. dampened red beech like for tops of planing workbenches but to use solid wood you have to know how to glue the stripes together to avoid warping. Also you need a jointer and a thicknesser (or a jointer hand plane and a lot of time and muscles 
)