The phrase "no problem" is a short version of "It was no problem," implying that it didn't cause the person any trouble or hardship to do the thing for which they are being thanked.
It could be construed as an act of humility or deference, because they are suggesting that the action they performed, and any inconvenience it may have caused them, are unimportant relative to the positive impact to the thanking party.
Fully unpacked, it goes like this:
"It was no problem for me to hold the door for you, because your ease of access is more important than me getting to my car faster."
Compare this with "You're welcome", which could be construed as an acknowledgement by the thanked party that they did do something worth thanking.
In an extreme case, this could be construed as more selfish or even arrogant, because the thanked party is allowing attention to be on them, instead of the other party.
"You're welcome to this open door, which I am holding open."
Obviously both connotations are usually very minor and mostly ignored; most of the time, people choose 'you're welcome' or 'no problem' because "It's just what you say when someone thanks you." I doubt many people actually think it's arrogant to say "you're welcome" unless it's said with a rude tone of voice. However, these implications may explain why 'no problem' has become more common, and could even be seen as a more polite reply.
Best Answer
You should use the second form. They're both correct, but only because 'welcome' is a funny word.
When you slime something, it becomes slimed.
When you pay something, it becomes paid.
When you welcome something, it becomes welcome!
Welcoming something imbues it with an fresh identity. It is now a guest. It is welcome. This is more serious than just saying something is now Xed because you did X to it.
The first form you provided is clearly a passive expression. It sounds like you are avoiding taking responsibility for the welcoming. The second form is not clearly a passive expression. It's idiomatic, anyway, and people will read it as you personally welcoming the challenge. Since the welcome in that case has become an intrinsic attribute of the challenge, the reader can safely assume it was you who granted it that status. With the first form, that assumption is not safe.
If you wish to be more bold you could say 'I have welcomed the challenge of growing my business'