Judo

One is a koshi-waza, the other a te-waza. They are indeed quite different in theory. While in actual fighting it might be hard to tell which technique was actually applied. But you should choose the one which feels better for you or whatever grip you can get. You don't get more points for throwing one or the other.

I mean if you look at competition results, it's very rare for someone to score with tsurikomi goshi, and it's just generally a more awkward throw to score with.

Generally it's not as powerful a throw as seoinage and if someone sees it coming it's easier to block by pulling backwards.

So if I had a choice I would always do seoinage.

one is a hip throw the other doesn't really use the hip as primary mechanic