I think it is subjective depending on the type of sol-gel and hydrogel. in terms of benefits, sol-gel material have the ability to entrap various functional molecules so it can be versatile tool for introducing desired functionality. for example better hydrophilicity which can help better cell attachment and growth.
Sol gels provide better mass transport of nutrition, flexibility and entrapment of carrier molecules as compared to hydrogels. They can also help in controlled release of active materials by phase change. Generally, solgels can undergo transition from solid phase to jelly like gel phases under external stimuli while hydrogels are already crosslinked stable structures. Also there are many hydrogels which are reversible sol-gels.
Additionally, the scaffolds/matrix (sol-gel, hydrogel, aerogel, hard polymeric/organic scaffolds etc.) for cells/tissue culture must be chosen on the basis of the compliance/stiffness required by the cells for e.g. bone cells require hard calcified scaffold, chondrocytes requires softer matrix than bones and neurons even softer. If you are culturing stem cells, the matrix stiffness may play an important role in the differentiation of cells. This is a good read which shows how matrix stiffness (from soft to hard matrix) controls stem cells fate.