Both have the same director and are about low ranking samurai who deal with love, impending poverty, and honour.
It's part of the same trilogy and deals with the same troubles of poor insignificant samurai during the waning years of the class hegemony. I'd also recommend "Love and Honour" with KimuTaku, the third in the trilogy.
'The Twilight Samurai' has a much more more quiet and sombre mood in comparison to 'Kakekomi,' which although has a similar aesthetic, is also light-hearted at times. Both films are set in the edo-period, and present men and women in an exceptionally interesting way, considering how most Japanese films portray and convey ideas in regards to gender roles (though Twilight Samurai is more subtle in this). 'The Twilight Samurai' is probably still a bit on the traditional side.