So, what's wrong with Joe?

[BRM13]

If you want to pick nits, I think the biggest one is his age.  He is much older than Lawrence.  He's even a year or two older than Lamar Jackson.  The reason this might matter is that I have read recently (The Athletic?) that QBs apparently take a big leap around age 23.  Burrow has already had his big leap.  Of course it was great one all the way to possibly the best QB season ever in college.  He doesn't really have to get a lot better; he just has to not get hurt.  If he was younger, there might still be one more 'growth spurt' in his game.  This is the real difference between Burrow and Lawrence.  Lawrence is more likely (but no sure thing) to get noticeably better than he is right now (e.g., improve touch, bring down high throws).

That said, they have to take Burrow #1.  Burrow's 'right now' is tremendous.  It has been amazing the past few games watching Burrow extend plays with his head up and throw accurately on the run.  He is also very good at slants and deep sideline throws (over the top, not out routes).  That accuracy is extremely valuable; I think he would kill in an NFL West Coast timing offense.  He isn't as fast as Kyler Murrary or Lamar Jackson, but he is plenty athletic enough to extend plays, pick up first downs, and generally distort defenses.   

Also, unlike our last two starting QBs, Palmer and Dalton, Burrow seems like a more classic team leader personality.  Considering how poorly this organization is run, locker room leaders are crucial (e.g., Whitworth or back when they last won a playoff game, Esiason).  Another thing I really like about Burrow is that he performed at an insanely high level in all his 'big' games. I don't know if this a real thing, but it seems like he has 'it' and his teammates respond to him.