Say if you are feeling anxious you feel "butterflies" in your stomach, or when despairing empty/ or heavy around your heart. If two people each reach the same degree of these emotions do they expirience the same feelings? And if not, what influences them?
You can start off from the clear observations of the neuroatypical and say no.
If you can reach the point where there are emotional experiences that simply do not happen for a small segment of the population, there is bound to be a continuum along which people not all the way there really are experiencing things quite differently.
Or you can look at the more physiologically normal mentally ill.
Even among those fairly close to normal, you can tell what kind of reactions a person may have in therapy by odd things like whether their experience of guilt or shame is 'subjectively empty' or 'subjectively full' or whether they just look at you funny when you try to find out. If we really shared an affectional base completely, it seems that we would all have both of those experiences, instead of a lot of us just not understanding the question. (Because the people for whom this answer is predictive do tend to understand it right away.)
It makes sense that the divergence can't be too great, because we share a vocabulary about it with so much detail. But to imagine that any two experiences are really exactly the same across individuals is probably not realistic. All of our emotions are tied up in different configurations of memory, and relatively few of those memories are really absolutely common between individuals.
I don't thing there needs to be too much difference in the constitution of our memories for me to have all of my fear, for instance, made up quite differently from all your fear, even at a sheerly physiological level. If I am prone to attack and you to freeze, in a general way that reflects a difference in personality, that probably goes along with a difference in internal experience that would be reflected in a slightly different physiological response.
In the human body, the brain consists of neurochemicals, neurons, and neurotransmitters. These are responsible for our emotional responses. Many other species have the same types of neurons that humans do. Even neurons we thought were unique only to humans are found in other species. I'm not aware of any types of neurons that humans have that aren't also found in other species in some form (e.g. Von Economo neurons). Our brains are obviously much, much more complex and have a much higher neuron density than other species, hence, why we have the level of cognitive functioning that we do.
Since we are all the same species, the basic biological properties and functions of our brains will be fundamentally similar between all humans. However, the brains of individuals exhibit a range of emotional responses. This range is determined by the level of brain activity in certain regions of the brain, but this is determined by the structure of an individual's brain. Some people feel emotions more strongly than others, some have no capacity to feel certain emotions, and so on. This varies as you would expect genetic variation between individuals.
The subjective experience of emotional experience is, therefore, very hard to qualify or quantify as with anything that has a subjective and value driven component (some people might think that seemingly mundane tasks are sublimely beautiful and so on). However, the most common methods of scientifically measuring emotional response include self-reports, physiological tests, and brain state scans.