MySQL vs PostgreSQL? Which should I choose for my Django project?

For whatever it's worth the the creators of Django recommend PostgreSQL.

If you're not tied to any legacy system and have the freedom to choose a database back-end, we recommend PostgreSQL, which achives a fine balance between cost, features, speed and stability. (The Definitive Guide to Django, p. 15)

As someone who recently switched a project from MySQL to Postgresql I don't regret the switch.

The main difference, from a Django point of view, is more rigorous constraint checking in Postgresql, which is a good thing, and also it's a bit more tedious to do manual schema changes (aka migrations).

There are probably 6 or so Django database migration applications out there and at least one doesn't support Postgresql. I don't consider this a disadvantage though because you can use one of the others or do them manually (which is what I prefer atm).

Full text search might be better supported for MySQL. MySQL has built-in full text search supported from within Django but it's pretty useless (no word stemming, phrase searching, etc.). I've used django-sphinx as a better option for full text searching in MySQL.

Full text searching is built-in with Postgresql 8.3 (earlier versions need TSearch module). Here's a good instructional blog post: Full-text searching in Django with PostgreSQL and tsearch2

large database with several hundred thousand entries,

This is not large database, it's very small one.

I'd choose PostgreSQL, because it has a lot more features. Most significant it this case: in PostgreSQL you can use Python as procedural language.