Lyceum and Gymnasium will give you better programs, teachers, resources, special subjects etc. They have fewer seats too obviously. And you don't have too many of them.
Common schools why being generally the same - also usually have different education levels. So before sendingg your kid to one of them you do a research - what kind of teachers does the school has, does it have football field or pool, maybe even you'll look into what have become of it's graduates.
When I was in school (1995-2005) The nearest school was... okay. It wasn't bad, but you don't really expect anything of it. Half boys older than 14 were smoking already, girls not giving two shits about studies, teachers who would just to their 9 to 17 routine. So I was attending Gymnasium 20 minutes away if you take a bus.