hand applique is just as durable as machine applique...as long as you use quality thread there should not be any problems with your appliques falling apart. as for the machine applique...i do both LOTS...and i HATE the invisible threads...i would be much more worried about that thread causing problems than i would ever worry about my hand work coming un-done. i made the mistake of quilting a quilt with invisible thread once...every time the quilt is washed more of the thread breaks, it became brittle...it is poky like those annoying clothing tags that poke you non-stop and drive you crazy till you remove them...and it was expensive name brand invisible thread...it is like sewing with fishing line and when it breaks it is poky-sharp...
it is usually recommended to try to match your thread to the applique fabric or a shade darker for the most invisible final outcome. when i machine applique i use colored thread, and use either a blanket stitch or very small zigzag- definitly faster than hand applique,