According to my current understanding, Bitcoin will always tend to increase its value because of being deflationary. But when BTC finally stabilizes and functions like other rare resources, such as gold, will its price be higher or lower than the current (around $250)?
Bitcoin is disinflationary not deflationary. A Subtle distinction, but an important one that reveals why we have seen capitulation during the last year despite it being a fantastic year by any other metric. We currently have ~10% inflation where almost 3600BTC have to be purchased daily to maintain price parity.
It won't stabilize anytime soon, expect massive volatility during the next 5 years, with another appreciating bubble within late 2015 till late 2016 at the latest.(If we don't see any adoption bubbles before than. ) This is because Inflation will drop to 5% in mid 2016.
Bitcoin may eventually become as stable as USD/Euro in 20 or more years with a large enough market cap.