Hi Sajad, it depends on what extruded product you are asking? It is a large category. If you are asking puff snacks, I think crispness/crunchiness is better description of the texture than hardness. Although in the end you might have to use hardness as a representative of crispness/crunchiness since it is easiest to measure.
To answer whether harder or softer is preferred, I believe you need a sensory test since different country/culture/marketing target will have different preference. Or if you have a local manufacturer, they might already have some sensory data.
Maybe the following paper may be of help to you to understand the sensory descriptors involved in dry foods such as extruded products. In table 4 crispness is described with different extruded products, in table 6 the same thing for crunchiness, and table 8 for crackliness. Score values of trained panel, sensory definitions and techniques of evaluation are also presented.
I couldn't agree more with Jibin He's answer, but I hope the article sent by Ana would provide you even better perspectives for the puff products texture characteristics. Generally, you have to take into account matters like who are your market target and what kind of market and population segment you are aiming at your product(s). Different market segment prefer different texture characteristics and, in some cases, it is also affected by the purpose of the products. For instance, breakfast cereals, snacks, or other kind of extruded products require differ texture/hardness characteristics. Non-puffed products also have various kind of texture characteristics, e.g whether it is cold or hot extrusion products, IMF and or high moisture extruded products, surimi-like or synthetic meat, they also demand certain texture (hardness) characteristic.
I agree with previous contributors. The question is a relative one, it depends on what you are producing and what it is intended for. Extruder can produce an array of materials which could come out expanded, condensed, dry, wet, semi-dry, food (breakfast cereal, snack food, all kinds of RTE, pasta, texturized protein, etc), animal feed (pet food, aquatic feed, cat food), cooked, partially cooked, etc. Seek out standard for texture measurement in textbooks or published literature on similar products.
Also, most equipment manufacturers provide help with regards to developing standard for using their equipment for various applications (common or new applications). They provide these in either a manual form (see equipment paper form or through help in the software that operates the equipment) or through their technical department - by you calling them and they guiding you through the process of protocol development to appropriately characterize your sample. All the best in your effort.
A good way to know what kind of texture is good for your extruded product is that you can use the optimization technique: buy a commercial product that you want to imitate and then measure its physical, physico-chemical and eating qualities. By using the optimization technique: RSM, you can know how hardness of your extruded product is desirable.