My Django project is going to be backed by a large database with several hundred thousand entries, and will need to support searching (I\'ll probably end up using djangosear
Even if Postgresql looks better, I find it has some performances issues with Django:
Postgresql is made to handle "long connections" (connection pooling, persistant connections, etc.)
MySQL is made to handle "short connections" (connect, do your queries, disconnect, has some performances issues with a lot of open connections)
The problem is that Django does not support connection pooling or persistant connection, it has to connect/disconnect to the database at each view call.
It will works with Postgresql, but connecting to a Postgresql cost a LOT more than connecting to a MySQL database (On Postgresql, each connection has it own process, it's a lot slower than just popping a new thread in MySQL).
Then you get some features like the Query Cache that can be really useful on some cases. (But you lost the superb text search of PostgreSQL)
There is a major licensing difference between the two db that will affect you if you ever intend to distribute code using the db. MySQL's client libraries are GPL and PostegreSQL's is under a BSD like license which might be easier to work with.
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
Go with whichever you're more familiar with. MySQL vs PostgreSQL is an endless war. Both of them are excellent database engines and both are being used by major sites. It really doesn't matter in practice.
To add to previous answers :
The FULLTEXT index in MySQL is a joke.
Other reasons not mentioned are the extremely smart query optimizer, large choice of join types (merge, hash, etc), hash aggregation, gist indexes on arrays, spatial search, etc which can result in extremely fast plans on very complicated queries.