Interesting thread.
I have done both and continue to do both in some sense.
I think which one is for you depends on what you like to do.
Production Support DBA can be ugly. Users can blast a table where a restore is required...unfortunately because you cannot restore just a table from a backup, well...you have to restore a database on a server which has enough space...and then bcp out the data.
While this seems easy -- you'll just have people calling you left and right wondering when it will get done.
Performance and Tuning can all of a sudden become a big issue on a given day. You have to grudgingly hack through bad code and determine why some sproc that ran "well" is taking a hit all of a sudden.
...on the bright side, doing this kind of prod support makes you into a better "developer DBA" -- you'll know for your app what tables to "backup" through BCP cause you'll understand how long a restore can take.
You'll write better sprocs, and more importantly create better indexes after having gone through tuning somebody else's bad sproc.
Personally - I prefer being a dev DBA because I like seeing the data -- and understanding how it can tell a story. Understand the data, and you can create a good db structure. Also - while you may encounter similar thing as a Prod DBA...for a dev dba...well...different types of data kind of make your job more interesting.
my two rupees 🙂