Rules-wise, I'd argue BT melee is probably fairly crude in comparison. Only targets adjacent and in front of a Mech can be kicked, but torso twist can allow punches to reach behind. 'Mechs can potentially kick other 'Mechs' heads off, but only if standing on something waist-high to begin with; otherwise, you can only kick the other 'Mech's legs. A missed kick also carries the risk of a failed piloting roll(you fall over, taking light damage and possibly hurting the MechWarrior).
For the most part, 'Mechs can punch, kick, or if needed, use makeshift clubs like severed 'Mech arms or uprooted trees(the latter do break after one use). Then there are purpose-built melee weapons like hatchets, but they're fairly rare outside of gaming arenas like on Solaris 7(not unheard of, but not common); the Clans shun them entirely(until DA, at least).
Jump Jets allow any standing 'Mech to attempt DFAs within their movement range(a Jump Jet-assisted stomp, essentially), but it's somewhat hard to actually land; furthermore, even if successful, it's not as powerful as one might think, the attacker will take armor damage to their legs(all other physical attacks that hit are "free" in that respect), and you're very likely to fail the modified piloting roll on landing afterwards.
Power-wise, it scales according to 'Mech weight. However(barring previously-mentioned TSM), not even an Atlas can punch a fully armored 'Mech head off(close, though; same damage as a standard PPC). Any Heavy(60-ton+) can deal enough damage through a kick to remove a head(12 damage). Hatchets and makeshift clubs deal as much damage as a kick(clubs do require two free hands to use, however).
It's really more of an opportunity-thing than something you actively try to do(though moving in for the chance to head-kick might well be worth it if you can catch someone standing next to a Level 1 hill).