The dissolution properties and bioactivity of bioactive glasses (BGs) are mainly determined by their glass network structure. Silicate BGs are the most famous representatives of BGs. However, borate BGs have gained increasing interest due to their faster degradation rate. By adding boron trioxide in the silicate network, borosilicate BGs can be fabricated with controlled degradation rates. Since the kind and amount of network former determines the resulting BG properties, the aim of this study was to examine the glass structure of silicate, borosilicate and borate BGs. Also, the effect of changing the network former on the ability to fabricate BG scaffolds by the foam replica method was investigated. The resulting silicate, borosilicate and borate scaffolds were further examined on their chemical, morphological, mechanical and bioactive properties. Structural analyses showed that the introduction of boron trioxide into silicate BGs leads to the depolymerization of the silicate network. Accordingly, the ion release profile and the ability to form hydroxyapatite of the different scaffolds changed. Thus, this study shows that tailored BG compositions with case-specific properties can be designed and used to fabricate 3D scaffolds for potential use in bone tissue engineering.