I just tested both clean mining and messy mining with my Blast I pick while flying.
For messy mining I was in a fresh God mine, and for clean I was in a fresh Titan mine.
Messy: Flying semi-slowly while directing my Blast pick in large circles.
Clean: Flying as fast as possible in straight lines and then turning around at the other end.
Messy: After 115 seconds of messy mining I accumulated 7870 mining experience, for an average of 68.4 xp/sec.
Clean: After 94 seconds of clean mining I accumulated 6710 mining experience, for an average of 71.4 xp/sec.
Verdict: Clean mining wins.
Disclaimer: This is by no means a thorough study of clean mining versus messy mining and mining speed will vary depending on your own individual clean or messy mining style.
I find messy mining to personally be more taxing on my mind and my mouse hand since I have to actively make sure that I am moving forward and that I am still in an area with material to mine. Messy mining is also very bothersome to other people in the same mine who might want to mine neatly but can't because you just ruined their mining path.
I like that with clean mining you have a clear objective of cleaning out an area completely in as little time as possible. At least with Blast, all you need to do is fly in a straight line, turn around at the end, and repeat. It's all very simple.
Semi-side note: Messy mining in the VIP mine is the absolute worst, especially when people leave once they've turned it to swiss cheese and can't get much money/minute any more.