Is "you are welcome" more polite than "no problem"?
What is the general proper reply to a thank-you?
First of all, this is always contracted "You're welcome" and is THE best response to thanks in any situation (NOT: you are, which would sound robotic)
No problem is quite familiar and not as "social" as you're welcome. An even more familiar version of this is no sweat.
Don't mention it is quite appropriate instead of you're welcome. If you went to significant trouble and someone thanks you, you can also respond with No trouble at all or my pleasure.
Just my personal opinion, You're welcome may be too formal in some cases, specially if it is not a workplace conversation. I've never seen anyone saying "No Problem" while talking to a client (Someone you're selling something to). In such cases I believe one should stick to "You're welcome." "No Problem" though an apt response, does not sound as gratifying as "You're welcome".
Some other responses could be "Sure!" or "You bet!". These two, as I understand make you sound more personable and should be used professionally only if you're very familiar with the other person. It has worked well for me around in Midwest and down south (mostly Texas). The location in this context could be important as well.
Nobody has said this yet, and I think it bears mention: "no problem" means "doing this for you didn't inconvenience me" and is often taken to mean "so you shouldn't feel any reluctance to make a similar request of me in the future."
Sometimes that's exactly what you mean to communicate. "Your paying my premium to rescue you from your fiasco was entirely welcome income to me! Let's do this all the time!" But I think more often than not, people err by downplaying the trouble they were put to by a request, and inadvertently set themselves up to be exploited by saying "no problem": telling people who ask favors of them that they should go go right ahead and ask more favors, instead of making clear that something was an imposition, but they did it anyway out of love, pity, or professionalism.
I have learned in business to never, ever say "no problem" unless I want a repeat performance of that situation. Someone comes to me with a rush job with no financial consideration? Asking me to bend the rules just very slightly for their benefit? If I indulge them and they thank me for it, the answer is "You're welcome", and never "No problem".
The vast majority of the answers here are very similar to the answers to When should “no problem” replace “you're welcome” as a response to “thank you”?, but this question is slightly different.
The asker wanted to know what "the general proper reply" is, not necessarily which response to use in which nuanced situation.
"The general proper reply" is "you're welcome". Sometimes another response, such as "no problem" might be somewhat better in the situation, but it can also be wrong sometimes, as pointed out in some of these answers. "You're Welcome" is always okay, even if it might seem a little too formal at times.
Note: "You are welcome" usually sounds a little forced. For a general solution, use the contracted "you're welcome".
To add one more option, "glad to help" and variants convey a positive and friendly response without diminishing one's effort, with similar connotation to "You're welcome" but a touch less formulaic and personal.
While I accept that it's what many have come so say, I find "no problem" somewhat circuitous, as it's more about the other person not having overstepped one's willingness, than about acknowledging or responding to their appreciation. As in - it was not a problem for me, or there is no problem between us because of this effort. Sometimes the effort really WAS a problem or difficult, in which cases "no problem" may be a social fiction; on the other hand, maybe it really wasn't much effort and this is trying to convey that. And often it's just an acquired local linguistic alias for the standard "you're welcome", said on autopilot to complete an interaction with no thought to it's actual meaning. So "no problem" is semantically very vague and at best indirect.
On the other hand, "you're welcome" said with some inflection to convey that it's not automatic, or "glad to help", are relatively direct and meaningful responses to appreciation.
Responding to "thank you" with "no problem" implies two connotations--one potentially negative and one positive:
I thought sufficiently little of your request that I might likely have never noticed had I not been thanked.
My handling of your request has not indebted you to me.
Additionally, in some business contexts, saying "no problem" may imply that the task didn't seem difficult. If the task was expected to be difficult, that would in turn suggest that either similar tasks might be done more efficiently by the person who handled the request than the person who would otherwise have performed them (and found them difficult), or that the person who handled the request misunderstood what was required and did not in fact do all the necessary steps. Either circumstance would merit investigation, and "no problem" may help trigger one.
Adding yet another possible reply: “anytime”.
The connotation, in my understanding, is that the other person may ask the speaker for similar help at any time in the future. It therefore carries some of the connotations of “no problem” and “it's been a pleasure”. I'd would consider it less formal and more cordial than “thank you”.
Regarding the first part of your question, I'd adapt to circumstances and the phrasing of the original thanks. To a polite “thank you” I'd answer “you're welcome” while for a less formal “thanks” I'd likely choose something less formal to reply with as well, e.g. the “no problem” you mentioned or the “anytime” from above.
In addition to these answers, I'd add that in situations where you haven't really done very much to deserve being thanked, "yup!" or "mmhmm!" (said with a pleasant tone) is often used as well, and is probably more common (at least in America) than either "no problem" or "you're welcome." This is a little informal but is frequently done even with strangers.
For example, if you hold a door for someone who is right behind you, or if you buy something at a cash register and the employee thanks you, this is probably more common than "you're welcome" or "no problem." I am not sure how polite this is, but you should know that it's common. (In the cash register situation, you can more politely respond "thank YOU.")
In American English, Hispanics often reply to "I'm sorry" with "No problem". This is because "No problema" is a Spanish idiom (used by Mexican-Americans and Central Americans) for accepting an apology.