As stated in other comments, I think the government does not care about the engagement, outside of the letters to get married upon entering the US, if you happen to mention that you are engaged, the way or manner of the engagement is really not important. Given a choice of K1 or Spousal visa, I would have opted for a spousal visa as the timeline outside of the country was about the same, but in the long term cheaper because many steps are not part of the process, (adjustment of status for example.) but this is something that is very personal to the couple making the decisions. My suggestion will always be to do your research on both options and then decide which one is best for you. Good luck.
