Multi-party computation is also a cool piece of technology. I think that I was always drawn to HE because it involves a completely trustless relationship with the server; in MPC, there's more a of a "m/n parties don't collude" assumption, that can be tricky to implement in practice. (Also side note: you can in theory perform arbitrary computation on encrypted data using FHE; the performance impact is really significant, like 100-10000x, but you can perform unlimited computation).
Surprisingly, these two concepts (MPC and HE) work quite well when combined! There are some computations each is suited to computing efficiently (linear for HE, non-linear for MPC), so when combined for ML, you get really good results. See this landmark paper and the follow on work: https://eprint.iacr.org/2018/073.pdf.