Acoustically there is no discernable difference so it just comes down to what you want to spend, if you care about weight, etc. I only use birch for my daily builds. For my competition stuff I use ac ply. It's basically cabinet grade plywood. Still as light as birch (almost) but costs less than mdf. The plys just aren't laminated that great.
If price is an issue, get mdf. If weight is an issue, get birch. If weight and
price is an issue, get ac ply.
AS far as working with both, they both have their good points and bad. I f'n hate how mdf splits and seems so weak, but it's a breeze to shape/router/sand. And if you are going to go with wood glue and clamps, this isn't an issue. I love the strength of birch and you can really get a bite on it with screws, but it's a little tougher to smooth.