I pretty much agree with most of the  comments here, except  the one about TBH being easier to fill.... That depends entirely on  the system you use.  Personally I use and  would stay with TBT  because  TBH definitely would not suit my filling...but i accept that I am likely a little unique in that.   I have a FC 3650 cart  and 63 foot bar and the  cart does put a LOT of weight on the tractor.

 I believe  TBH is dead weight and harder to pull,  and does tend to pull  the bar sideways on slopes. 

The issue of  leaving tracks with TBH depends entirely on your soil type and conditions.

For me  the issue of visibility of the bar sounds like an issue, but  since running airseeders since 1985 really hasnt been...But again..that is entirely dependant on  your own conditions.

There are two other benefits  to TBT not so far mentioned....       

For those of us that use  the cart  with a spreader bar for post  application of whatever product then TBT is far more suitable....  but very likely of no interest to you.

The other issue is i think pretty much EVERY manufacturer I have seen with TBH in these parts  have had issues at some stage with  the caster assembly come adrift   and basically destroying the manifold as they  go under the  cart.   
Admittedly this issue dates back some years now, and may  or may not  be relevant any more.

TBT for me  ,,,always