I like the Corolla better

These are two different categories of hybrids. One is a plug in hybrid, the other is a regular hybrid. 

If you want to plug it in, get the prime. 

If you don’t want to deal with plugging it in, get the Corolla hybrid or the regular Prius. 

As far as reliability, both the Prius and the Corolla are built in the same platform, so they are for all intents and purposes the same car. 

Prius is slightly more aerodynamic. And has a hatchback. Corolla has a trunk. Some find either one useful. 

Well, realize the prius prime is a plug-in hybrid and the corolla hybrid is a regular hybrid. I would go Corolla hybrid hands down even though it's not built in Japan, it's more affordable, still gets great gas mileage, and it looks way better. The Prius is pretty ugly, not as desirable as previous generations, expensive, and it's pretty outdated compared to the latest Toyota Hybrids especially the Rav4 Prime (personally my favourite Toyota on sale rn).