Any big problems that hold it (and you) back?
On the one hand, I'd like some very optimistic numbers to help sell the idea of dropping $8K on software up the ladder
There are some bugs in Altium, just like all software. Some bugs get fixed quickly, others do not.
Like all powerful software, the biggest hurdle is the learning curve.
Altium's price will rise by US$2000 in June, so don't delay if you are going down this track. Remember Altium will slug you another US$1850 for annual support that you have to pay. Remember also that you will have to continue to pay this every year if you want access to the "Component Vault" which has been extensively used since AD14 was released (the component libraries that come with AD14 were significantly reduced over those in AD13).
If you want pcb design software that is quite powerful & certainly easier to drive than Eagle, consider Proteus. US$2000 will buy you the unlimited version & there are some fairly cheap pin restricted versions plus a demo available (save is disabled in the demo package).
Owning Altium & Diptrace & having used Proteus for a contracted design job 18 months ago (package owned by the company I did the design work for), I was pleasantly surprised at its ease of use & the features offered.
You need to look carefully at how much pcb design work you do & what features you require to complete it.
Also take a look at how big the bulge is in your wallet.
Proteus has both an auto-placer & an auto-router & you can add the powerful Electra autorouter (just like you would use in Altium Designer) for US$400.
Just my 2c worth.