I mentioned it in a different comment, but it has been put forward before that we may feel less intense emotions exactly because of our extra reasoning capabilities.
One example put forward is that we understand an ending to our pain. For some animals, they may not know all possible ends to their feelings, and thus might feel intense sensations of fear, pain, helplessness, etc. There have been some horrific experiments done in the past to illustrate that many animal species learn that they have no way out of painful situations and just give up when options are exhausted. A human might endure knowing that it is just an experiment, but a dog knows no reason that something like an electric shock experiment would eventually stop. Our ability to self sooth, whether it is irrational or not, seems to help us in these situations.
This is a long one, I apologize for any unnecessary verbosity, but I find this conversation to be important and a short comment just doesn't do it justice.
Anyway, it seems that you are taking a somewhat antiquated, but still prevalent view on consciousness - the more "old-school" behaviorist approach that is. It also seems like there's a few discussions happening on this comment thread. Your original post has an assumption in that humans have an objectively "higher" state of awareness followed up with a question on whether or not this preconceived idea would impact the intensity of emotions. I'll try to keep this information in mind with what I say.
To better communicate what I want to say first, I'll take your first statement to be true, regardless of further discussion. I more thoroughly explained the existing evidence in response to another person here. But to summarize, our ability to analyze stored information, to the extent we can, seems to help us cope with intense feelings. This gives the answer to your question: probably not - other animals may feel equal or more intense emotions by measurable standards.
But, hey, we're onto a slightly different topic, so why not talk about that. You've posited that the human capability to ask "why" gives us an objectively higher state of awareness. This statement is a tough one to put forward, even for the most renowned philosophers, who have thought this through far more than I have. It runs into road blocks with questions like:
Until we answer these questions, among many others, I see no reason to confirm that our ability to ask "why" (self-reflection), is the go-to for determining consciousness. Nor can I find a reason to let this impact my actions. I see it more as an interesting distinction that might exist between species. I do not know how much that distinction is, but it's something to think about. But again, I feel that matters just about as much as other capabilities like speech, hearing, reading, thermal control, movement, empathy, etc. They seem to be helpful evolutionary adaptations, but I hold none of them higher than the other. After all, their importance is impacted by my personal bias. I imagine bats would hate to lose echolocation, yet I, a being who holds no importance in echolocation, am much more scared of losing my ocular vision.
This is off-topic, but the above thought process has led me to consider consciousness more carefully in my actions. My current approach is that I ought to value another being for their individual abilities and desires. Meaning, I value any other human's want to have subjective societal values like the right to vote. However, I can reasonably assume a pig, chicken, dog, cat, or any other non-human animal does not care about voting. Rather, many of them seem to do things like avoid pain, comfort others (empathy - some family, some others in a herd, some just anyone they are near), and seek hedonistic joys like having their skin scratched/muscles massaged, eating nutritional foods, and playing with one another (again, to some extent). So, I will consider their subjective wants to the best of my abilities.
That's my current take at least. It seems the more I learn from others, the less confident I feel about any particular meta-ethical approach to understanding. --