Comparative analysis of the rheological behavior of fat analogues and adipose tissue is useful as a means of better understanding the behavior of these ingredients in reformulation and cooking processes. Fat mimicking oleogels were developed based on various enzymatically glycerolized oils and ethylcellulose (EC) of differing molecular weights at a 5% concentration. The dynamic rheological behavior of the oleogels and adipose tissue of different origins (pork, beef, lamb) was studied via amplitude and frequency sweeps. Glycerolized oils and their oleogels behaved as solid-like materials, as elastic moduli were greater than viscous moduli throughout the linear viscoelastic region. Addition of EC produced a more deformable and cohesive product. Solid fat content was a dominant contributor to viscoelastic properties of GP-EC oleogels. Oil systems containing higher levels of saturated fatty acids such as palm olein and shea olein exhibited a more rigid structure, with stiffness comparable to that of pork and beef adipose tissue. Whereas tigernut, peanut, and rice bran oil oleogels were significantly softer and more deformable. Temperature sweep experiments were conducted to visualize the general softening behavior during cooking. The melting of fat dramatically softened both adipose tissue and oleogels. However, the microstructure of adipose tissue was intricately linked to its protein matrix at elevated temperatures, leading to substantial increase of elasticity from 50 °C to 80 °C. Oleogels exhibited thixotropic behavior by recovering their elasticity and functionality over time once the force is removed. This characteristic minimizes the shear related issues during and after the gel-setting process.