Recent years have seen the dynamic development of methods for functionalizing the surface of implants using biomaterials that can mimic the physical and mechanical nature of native tissue, prevent the formation of bacterial biofilm, promote osteoconduction, and have the ability to sustain cell proliferation. One of the concepts for achieving this goal, which is presented in this work, is to functionalize the surface of NiTi shape memory alloy by an atypical glass-like nanocomposite that consists of SiO2-TiO2 with silver nanoparticles. However, determining the potential medical uses of bio(nano)coating prepared in this way requires an analysis of its surface roughness, tribology, or wettability, especially in the context of the commonly used reference coat-forming hydroxyapatite (HAp). According to our results, the surface roughness ranged between (112 ± 3) nm (Ag-SiO2)—(141 ± 5) nm (HAp), the water contact angle was in the range (74.8 ± 1.6)° (Ag-SiO2)—(70.6 ± 1.2)° (HAp), while the surface free energy was in the range of 45.4 mJ/m2 (Ag-SiO2)—46.8 mJ/m2 (HAp). The adhesive force and friction coefficient were determined to be 1.04 (Ag-SiO2)—1.14 (HAp) and 0.247 ± 0.012 (Ag-SiO2) and 0.397 ± 0.034 (HAp), respectively. The chemical data showed that the release of the metal, mainly Ni from the covered NiTi substrate or Ag from Ag-SiO2 coating had a negligible effect. It was revealed that the NiTi alloy that was coated with Ag-SiO2 did not favor the formation of E. coli or S. aureus biofilm compared to the HAp-coated alloy. Moreover, both approaches to surface functionalization indicated good viability of the normal human dermal fibroblast and osteoblast cells and confirmed the high osteoconductive features of the biomaterial. The similarities of both types of coat-forming materials indicate an excellent potential of the silver-silica composite as a new material for the functionalization of the surface of a biomaterial and the development of a new type of functionalized implants.