My reply is 100% based on experience. I was in exactly the situation you're in, and I think I chose wrong.
My first full season of playing BB I promoted quite easily out of Div IV. I had some good young prospects, but I wanted to train the next superstar. I sold my young players and bought some excellent 18 year old players with the intention of tanking in Div III and getting a "great" draft pick. My plan only kind of worked - I got relegated, but I didn't end up with nearly the draft that I had hoped. I sold my two picks for about 500k total and figured, "okay, no big deal, I'll just pop back up to Div III next season." Unfortunately, there turned out be another solid team in my Div IV league. I lost, and now here I am in Div IV again! I am sooooo missing the extra money that comes with being in a higher division. I got fantastic deals on my staff, so I don't want to get rid of them because they'll be reasonably priced for the next couple seasons. However, I'm only making about 20k a week right now - just treading water.
Morale of the story - stay up! The extra money is worth it, and if you intentionally drop down, your stay down may be longer than you predict!
cheers!