Gelatine melts at a lower temperature and has a much better mouthfeel for most of these traditional recipes. It is creamy and adds body to a stock or sauce. Agar is brittle and requires a higher temperature to set. Agar would be a good choice for something where you want it to stay in a particular shape, but it is much more of a one-trick pony when it comes to cooking. Each can act as a poor man's version of the other, but neither really hits the same features as the other.

Agar is great for a gel, especially one you want to stand up to a bit of heat and remain stable at room temp, and I would always reach for it instead of gelatine when doing most desserts or pastry work. OTOH I would only use it in a sauce if I needed to accommodate a vegan guest.

> I would only use it in a sauce if I needed to accommodate a vegan guest.

As an alternative, I've found methylcellulose to be pretty good for thickening my vegan homemade sauces (mainly tried it because I use it for other stuff, like fakemeat homemade protein sources). That's for homemade mayo or the like; for sauces in stews and similar, flour does the job - though US cooks seem obsessed by cornstarch instead for that use case.