From the mouths of my customers here are some pros and cons I've heard about each setup:
TBT's are easier to transport and safer because you don't have that cart (which ideally is empty during transport, but realistically always seems to have some grain or fertilizer in it) with it's extra weight back there, making control of the tractor and implement more challenging (and dangerous).
TBT's don't drag that heavy air cart over the seed you've just planted.
TBH's allow better visibility of the seeding tool. Now, I have no-till (1890 JD) customers tell me that visibility shouldn't really be an issue, because those no till openers should go through anything and not plug. However on a hoe drill, planting in residue, I can see where this could be more of an issue.
TBH's allow a bigger cart option than TBT's (at least with Deere, 270 bushels to 430). Of course, then you have more weight when the cart is loaded, passing over the freshly sewn seed.
TBT's compact the ground in front of the seeding tool, thereby causing premature wear on the opener disks that follow the tractor tires/tracks and the cart tires.
Also on the subject of compaction, I had a farmer tell me that the weight of the cart really isn't a concern in heavier residue, for the fact that the residue acts as a "pad" and helps cushion the weight of the cart as it passes over the soil.
Those are some of the points air seeding customers have made to me. I think it all boils down to doing lots of research and determining what works best for your operation. Hope this helps.