The main advantage of the style with the lip under the bucket is that it gives you a "flat-bottom". This is beneficial if you do a lot of backdragging.
And I am no expert and I have not actually used either style, but just looking at them and the design of the teeth, I cant help but think the "flat-bottom" style wont dig quite as good. But that is just going off of looks.
Personally, on mine, I just bought direct bolt on teeth. 8 of them was only $70 delivered. And while I cant remove them quite as easy as a tooth bar, they are still removable. But I dont ever see me taking them off. And I know they arent as strong as a tooth bar, because they dont add that second cutting edge for strength, but my loader isnt exactally a super strong loader. And I have yet to have any issues.
The two reasons I went this route were because of existing fork pockets in the corners of my bucket (for lifting logs and such), and price. I just could't justify $300 for a tooth bar that I would still have to modify to make work.