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As a contractor who is not a drywall taper I have the opportunity to see the professionals at work. But I am like you and drywall and tape my own home. I find the mesh is easier to work with as you apply it first then the taping compound after. If you use tape you have to apply a layer of mud, then run the tape and pull the excess mud, and then build up coats over the top. With the mesh you have to build up but it seems easier to me. One word of warning, if you do not apply enough coats of tape compound over the mesh, when you sand the mesh will show through and paint will not hide it.
As far as stronger, I think the mesh is because the tape compound penetrates through the mesh as opposed to tape which is on top and bottom.
paper tape is for regular joints and corners, which id say is most commonly used, the only time i use mess tape is if there is a crack on a wall that i cant float out really wide, as i would have to do if i used paper take, mess does blend in much easier than paper, strength wise if there both do correctly i dont see one better than the other. also if youve not done alot of taping id say to use the mess since its much more forgiving on the first coat.