The elasticity of substitution of production factors derived from empirical data depends on the data. In the case of simple production, you can estimate the production function (fit your data to the functional form of the production function) and from it derive the elasticity of substitution and other functional parameters.
The elasticity of substitution in the case of a production function (accounting for output) has it's roots in the classical consumption function (accounting for utility), as you mention.
Empirical studies are plenty and the numerical results vary depending on country, industry (aggregate level) or type of company (micro level). However, the robustness of the results may not be up to par, because aggregate (and otherwise), especially neoclassical, production functions are subject to numerous restrictions and assumptions.
For empirical studies you can start here Chirinko R., Fazzari S., Meyer A., 2004
In the case of utility (elasticity of substitution in consumption function), I don't know of any empirical studies. I'm not one to be asked this, but my first hunch is - additive utility is a REALLY strong assumption. Classical and austrian economists have argued that utility is subjective. So, numerical studies of elasticities of substitution in consumption would have to be verry biased.