Does kickboxing allow low kicks?
It depends which one. Under WAKO Low Kick and K-1 rules and in GLORY and K-1 promotions, yes — the thigh is a legal target and the shin may be used. Under WAKO Full Contact rules, kicks to the hip, knee and shin are fouls, and every kick must land above the waist. A gym that trains for Full Contact competition will not kick your legs; one that trains for Low Kick will kick them a great deal.
Is K-1 one rule set?
No. WAKO publishes a K-1 chapter, GLORY publishes its own rulebook, and K-1 World Grand Prix publishes another. They agree on knees and on banning elbows, and disagree on the rest: GLORY bans all sweeps and throws and bans linear kicks to the leg; the K-1 promotion bans all grabbing; a national federation can allow ankle-level sweeps under K-1 rules. Ask which rulebook before assuming anything.
What changes when a Kyokushin fighter moves to kickboxing?
The account from people who made the move is consistent: rhythm, balance, kicks, recovery after a missed kick and conditioning come with them. What kickboxing adds is head movement, the defence of a punch to the face, hooks, combinations and lateral movement. One published opinion piece argues that years of hard sparring without head punches dull the reaction to them; the practitioners who cross over describe the same gap and close it with drills.
Which is more demanding physically?
Knockdown karate demands sustained contact to the body and legs without pauses, bare-handed. Kickboxing demands three or five explosive rounds with a guard that cannot drop, in gloves that let the head be a target. Each side reports being surprised by the other's version of fatigue.
Which is better for self-defense?
Kickboxing trains the defence of a hand to the face, which knockdown competition does not; Kyokushin trains taking impact without gloves, which kickboxing does not. No study compares the two on real outcomes. The question is addressed on the page about Kyokushin and self-defense.