I've been a relatively mild-mannered open source advocate for over 20 years now, and have been running Linux for all of it. My first DBA job was with Postgres (6 or 7, ~12 years ago now!) and now Oracle. This is all about databases, completely ignoring the application related acquisitions they've made in the last decade...
A lot of difference I see and is evident from the discussions here is that Oracle usually has the features earlier (not always, but yes, usually). The earliest example I've witnessed is Postgres' Write-Ahead Logging, which was definitely cool, but Oracle were there first. More recently, with 11gR2 you have advanced compression (pay $$$$ and it will store all your data compressed if you want) and with 12c there are a bunch of features that make me drool. Pluggable databases is just one of them.
Again, not entirely sure about Postgres, but Oracle build a lot of instrumentation into the database software itself. Tracing custom events is a great way of profiling your application as well as database deficiencies. Pay for the license to unlock the full power of ASH or AWR and you have a great deal of ability to see exactly what's going on and figure out how best to resolve any performance issues. The best bit is that this instrumentation doesn't make the database run like a dog. A few percent overhead gives you a lot of debugging power, and it's ALWAYS turned on with basic event tracking always happening anyway. But you can add MOAR.
I see some impressive performance on Oracle databases these days, but not entirely convinced that Postgres cannot meet them. But then, Oracle can run on anything from 32 bit x86 to some seriously beefy hardware (and when it does, it runs well). I'm not entirely sure about Postgres, but I know Oracle has been compiled for RISC architecture (Power, SPARC, HPUX, others??) for a long time. These days they to lean towards x86 - and will even sell you a "database machine" (google for Exadata). This extends to scaling out on any of the supported architectures with their cluster software (Grid Infrastructure) these days, which is quite mature now. Again, Postgres probably does this, but each generation sees a significant improvement for Oracle.
Having said all that, leading edge can also be bleeding edge... The biggest problem for me with Oracle continues to be the time it takes to resolve software bugs combined with their support infrastructure. While it usually gets there in the end, for the price you pay for enterprise support one might expect quicker resolution if you happen to be the first person to hit upon a specific problem. Unfortunately this tends to tie with the need to certify with all the Oracle applications they release and support. The one and only bug I reported when I was a Postgres DBA was around a date calculation issue - from the behaviour I reported it was tracked down and patched in ~ 2 days, and I had a workaround for the meantime anyway.
Oracle have also done some cool stuff in the open source domain with OCFS (and now OCFS2) and the free domain with their base GI cluster software, as well as the plain cool domain with ASM (dynamically manageable disk pooling with Stripe And Mirror Everything methodology providing solid data robustness) and ACFS which lets you carve out clustered POSIX compliant filesystems on top of ASM at will. This all helps with scaling (don't need OCFS2 now if you use ACFS tho).
Hmmm, it seems they really are turning me to the dark side.... heeellllllppppp!!!!