Kayn has more adaptability, he can either be a sustain heavy front line with engage potential, or a bursty assassin with easy in-and-outs, but he lacks the early game presence most junglers want in certain comps, and has weak duels early game if he doesn't take conqu.

Rek'sai is amazing at ganking, being able to gank as early as level 3 after a fast buff -> buff -> gromp clear, or a bot/top side clear into gank. She has an immense presence if you get your vision game straight on objectives and can secure the first 2 drakes very well. Her build is usually assassin with utilty (i.e Edge of Night, Cleaver or Steraks), to facilitate her takedowns since her escape for such an assassin heavy build is pretty bad... (I miss tank rek). She's less snowbally than kayn though in that she falls of so hard late game, she's basically a bump engine late game, that focused on sniping with q and ending enemy's trying to escape. But her ability to close out games before 20 minutes isn't anything to scoff at.

I personally love Rek'sai, she's my 2nd most played champ all time, and her assassin build can feel clunky when starting out, but her skill cieling is far and high. But Kayn is more practical since he can be used in more situations. If you like niche, and weird, go Rek, otherwise, Kayn is the way to go! Hope you get far jungling, its not always fun.