I'm sorry not to go with the flow, but I'd argue that ux is, largely, neither.
On Science
From Wikipedia (emphasis mine):
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. In an older and closely related meaning, "science" also refers to a body of knowledge itself, of the type that can be rationally explained and reliably applied.
It then goes on to say:
During the Islamic Golden Age, the foundation for the scientific method was laid, which emphasized experimental data and reproducibility of its results.
And then:
However, "science" has also continued to be used in a broad sense to denote reliable and teachable knowledge about a topic, as reflected in modern terms like library science or computer science.
So, as one would expect, there isn't one strict meaning to the word. Most importantly, there's the distinction between the body of knowledge and the process; and there's also the use of the (relative) term reliable and the more rigorous scientific method.
But I'd argue, that the critical term in all these definitions is the scientific method - without it, we'd live in a world of relative certainty and a very problematic spectrum of reliability, which can also be subjective.
The 'science' of Scottish independence
An example would be appropriate here. The latest poll results of the TNS-BMRB research group with regards to the Scottish independence are presented in the following graph (source):
Other research groups have produced slightly different results, and there is a dedicated page explaining the methodology employed, including some warnings about the reliability of the results.
Now compared to most UX research activities, all these research groups had in their disposal a larger sample size (1000 people), and they employed a method that is statistically more rigorous. Needless to say, scientific tools were applied in the course of this research.
But can you say with next-to-certainty that had the vote took place on the same day as each poll, the poll would be correct, even within the margin of error defined? The fact is that it often happend in the past that similar polls were well off the mark from the actual vote results.
In other words, despite employing a systematic scientific tools, the results cannot be considered as scientifically valid. What's more, the poll does not allow in any way making predictions.
So despite employing scientific tools (and a more rigorous method than in most UX research), I still wouldn't call this true science.
Flawed Science
As far as UX goes, there is even more to argue that even the application of scientific tools within UX is heavily flawed. I'd spell it out myself had it not been to Jakob Nielsen who has written an excellent article on the topic. The summary goes:
Number fetishism leads usability studies astray by focusing on statistical analyses that are often false, biased, misleading, or overly narrow.
It has to be asserted that while people like me believe that the field of evaluation in UX is flawed to the bone (yet one would be fool to overlook its usefulness), the field of cognition (which is based on real science) and other scientific disciplines (such as mathematical network analysis) could prevail in the future to yield altogether more reliable results. But this is still an application of scientific tools, which I don't think suffice to award a field as scientific in the broader sense (it is in the narrower sense, like the field of political science).
On the science of the God particle
The Scottish independence example is in contrast to the finding of the Higgs boson, where the scientific method was applied with the high certainty threshold of 99.999%. In other words, we know, nearly for certain, that the particle does exist (and while a story for another day, empirical science also has it that there is no way to prove something with 100% certainty, so 99.999% is sufficiently reliable).
This is true science in my view.
When UX is a science
Given the definitions above, there is an exception where UX is a science - and that's when PHD students or researchers in big companies do follow the scientific methods, with an hypothesis, statistically valid results, reproduction by unrelated research groups, etc.
But, that's not what UX practitioners really do in their daily job.
On Art
From Google's define:
The expression or application of human creative skill and imagination... producing works to be appreciated primarily for their beauty or emotional power.
OK, so on the one hand, when you come to make most design decisions (in IA, for instance) neither creativity skill, nor beauty or emotional power is involved - you want to hit the common denominator and hope to base your decisions on either data or reason. In other words, designing an interface is not quite like composing a song or painting a painting.
On creativity
However, creative skill is required during the (conceptual) design process, but unlike with arts, your creativity only serves to produce options which are then rationally analysed. This is markedly different from artists who are often purely emotionally driven.
On emotional design
But what about emotional design, which is such a big part of UX nowadays?
I'd argue that you have to make a distinction between the emotional effect of artworks, which is attributed to an illusive ability of an artist to plunk the right strings with the audience within a cultural context (and context, in general, plays a massive part in arts as the painting below demonstrates, by one of the greatest 20th century painters Jackson Pollock), and the intentional and calculated attempts of UX designers to incite an emotional response from users by applying knowledge of cognition.
When UX is an art
If you frequently visit Pinterest or Dribbble, it would be hard to deny the artistic values of many of the designs there. Most of this art is done by graphic designers, a work some consider to fall under the UX umbrella. If such is the nature of the work produced by a UX designer, then it is art indeed.
On "feeling it"
You said you make some decisions "because it feels right", which I believe can be more accurately described as "it is your intuition".
With the dual-process theory (DPT) becoming more an more pivotal to our understanding of the brain, in the world of psychology intuitions are often simply considered as the workings of the unconscious brain (system 1 in DPT).
In essence, substantial experience in a specific field (or situation) results in an automatic decision from the unconscious brain that is so definite that your conscious brain gets it with the tag "No need to reason this one out".
Perhaps the greatest example of this process can be found in an event that ran during February 1996, where Garry Kasparov has beaten IBM's Deep Blue. The former was only capable of consciously processing 3 positions per second, where the latter could process more than 100,000,000. Yet chess grandmasters game is nearly solely based on System 1 - in other words, their game is nearly fully based on intuitions, the result of a neural network capable of far more than 100,000,000 calculation per second. Chess grandmasters often cannot explain their moves (and even if they do it is believed to be retrospective reasoning) - it is a lot of complex unconscious, rather that conscious reason that guides them.
This may seem highly impressive, but you are doing the same thing at this very moment. If I'd ask you what you understand from this sentence:
"John had an ice-cream and really liked it"
you'd probably say something very similar to the sentence. But if I'll then start bombarding you with questions like "How do you know John means a person?" or "How do you know what 'likes' mean" or "How do you know 'it' refers to the ice-cream" (and so on), you'd find it hard to answer these - you have little idea why you understand language, it is mostly system 1 process.
You may think that this relates to art - after all, it has already been mentioned that artists are typically guided by intuitions. But you are also guided by intuitions when flicking through TV channels and seeing something that "you feel" could be good. There is nothing artistic about it, nor any creativity or imagination involved.
So being guided by intuitions alone is neither art nor science.
