Doesn't look like there's any difference on the basic level (well, except the AP cost):
http://fallout.gamepedia.com/Unarmed#Unarmed_skill_attacks
There's a whole list in there of what they do;
[TABLE="class: va-table va-table-center va-table-full, width: 960"]
[TR]
[TD="align: center"]Punch[/TD]
[TD="align: center"]None[/TD]
[TD="align: center"]Base damage[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]-[/TD]
[/TR]
[TR]
[TD="align: center"]Strong Punch[/TD]
[TD="align: center"]Unarmed 55%, Agility 6[/TD]
[TD="align: center"]+3[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]-[/TD]
[/TR]
[TR]
[TD="align: center"]Hammer Punch[/TD]
[TD="align: center"]Unarmed 75%, Agility 6, Strength 5, level 6[/TD]
[TD="align: center"]+5[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]+5%[/TD]
[/TR]
[TR]
[TD="align: center"]Haymaker[/TD]
[TD="align: center"]Unarmed 100%, Agility 7, Strength 5, level 9[/TD]
[TD="align: center"]+7[/TD]
[TD="align: center"]3[/TD]
[TD="align: center"]+15%[/TD]
[/TR]
[TR]
[TH="bgcolor: #C9D0AC, colspan: 5"]Secondary punch attacks[/TH]
[/TR]
[TR]
[TD="align: center"]Jab[/TD]
[TD="align: center"]Unarmed 75%, Agility 7, Strength 5, level 5[/TD]
[TD="align: center"]+5 (+3 in 1.02d)[/TD]
[TD="align: center"]6 (3 in 1.02d)[/TD]
[TD="align: center"]+5% (+10% in 1.02d)[/TD]
[/TR]
[TR]
[TD="align: center"]Palm Strike[/TD]
[TD="align: center"]Unarmed 115%, Agility 7, Strength 5, level 12[/TD]
[TD="align: center"]+7, armor piercing[/TD]
[TD="align: center"]6[/TD]
[TD="align: center"]+15%[/TD]
[/TR]
[TR]
[TD="align: center"]Piercing Strike[/TD]
[TD="align: center"]Unarmed 130%, Agility 7, Strength 5, Level 16[/TD]
[TD="align: center"]+10, armor piercing[/TD]
[TD="align: center"]8[/TD]
[TD="align: center"]+40%[/TD]
[/TR]
[TR]
[TH="bgcolor: #C9D0AC, colspan: 5"]Primary kick attacks[/TH]
[/TR]
[TR]
[TD="align: center"]Kick[/TD]
[TD="align: center"]None[/TD]
[TD="align: center"]Base damage[/TD]
[TD="align: center"]4[/TD]
[TD="align: center"]-[/TD]
[/TR]
[TR]
[TD="align: center"]Strong Kick[/TD]
[TD="align: center"]Unarmed 40%, Agility 6[/TD]
[TD="align: center"]+5[/TD]
[TD="align: center"]4[/TD]
[TD="align: center"]-[/TD]
[/TR]
[TR]
[TD="align: center"]Snap Kick[/TD]
[TD="align: center"]Unarmed 60%, Agility 6, Level 6[/TD]
[TD="align: center"]+7[/TD]
[TD="align: center"]4[/TD]
[TD="align: center"]-[/TD]
[/TR]
[TR]
[TD="align: center"]Power Kick[/TD]
[TD="align: center"]Unarmed 80%, Agility 6, Strength 6, Level 9[/TD]
[TD="align: center"]+9[/TD]
[TD="align: center"]4[/TD]
[TD="align: center"]+5%[/TD]
[/TR]
[TR]
[TH="bgcolor: #C9D0AC, colspan: 5"]Secondary kick attacks[/TH]
[/TR]
[TR]
[TD="align: center"]Hip Kick[/TD]
[TD="align: center"]Unarmed 60%, Agility 7, Strength 6, Level 6[/TD]
[TD="align: center"]+7[/TD]
[TD="align: center"]7[/TD]
[TD="align: center"]-[/TD]
[/TR]
[TR]
[TD="align: center"]Hook Kick[/TD]
[TD="align: center"]Unarmed 100%, Agility 7, Strength 6, Level 12[/TD]
[TD="align: center"]+9, armor piercing[/TD]
[TD="align: center"]7[/TD]
[TD="align: center"]+10%[/TD]
[/TR]
[TR]
[TD="align: center"]Piercing Kick[/TD]
[TD="align: center"]Unarmed 125%, Agility 8, Strength 6, Level 15[/TD]
[TD="align: center"]+12, armor piercing[/TD]
[TD="align: center"]9[/TD]
[TD="align: center"]+50%[/TD]
[/TR]
[/TABLE]
The major problem is that anyone in their right mind that does an unarmed build will almost certainly pick up a Power Fist, and later the Mk II, which is a punch only weapon and does significantly more damage than any of the other attacks. Then you couple that with the efficiency of punch over kick when it comes to AP (especially when you have Bonus HtH Attacks). The only benefit I can see with some of those is the armor piercing, but I'm guessing Spiked Knuckles solves that problem, and they're relatively easy to get. Also, I personally find it pretty annoying when someone gets knocked back, and yes that is a benefit of kick.