Depends on how the chip is bonded to the PCB, not all finishes are compatible with all processes.
Also OSP is actually pretty damn good these days, we started using it as standard for prototyping, additionally you need no obnoxious chemicals other than a short micro-etch pre-dip after resist stripping. The main issue you see with a lot of OSPs is that you can't really put them in a spray installation (they do exist though), but you need an "immersion" system instead. But overall ENIG has a few issues, the nickel plating is quite porous and doesn't really protect the copper underneath that well. And the thin gold flash basically does nothing, and if you have any strong acids in your plating bath (and yes, you do) these can corrode the nickel and copper underneath. If you want to see how "good" the ENIG plating is, dump a piece of scrap PCB in some sulphuric acid and make a cut-through afterwards, you'll see some interesting things happening. But BGA balls are rather small, so that thin 100 nm gold flash might contribute a considerable portion. (9 micron copper + 1 micron nickel + 0.1 micron gold) If you then consider the solder will normally leach away all the gold on the pads things ain't pretty. Additionally you get to play with cyanide to do ENIG plating, so there's also that little problem.
The main reason to still use ENIG is that it's very flat and very cheap because everyone in Shenzen and their mother does it, OSP often involves manual processing due to the above caveats. Many board houses don't get enough OSP volume to invest in a line for it, so it's still done in trays or even beakers. ENIG on the other hand it's a case of stick the panel in the line and wait until it comes out. Process control is also an important factor to making ENIG work, any mistake and any impurity in the plating solutions will cause solder joint defects later on. And lets just say, you haven't lived until you've been in a backroom PCB manufacturing line in rural China; and if you have been there it'll shorten said life by a few months most likely. I recommend a good pair of acid resistant safety shoes/boots if you do wish to experience it, not that it's worth recommending in the first place.
But you can find many overviews on these things, I think there's a pretty good description in Coombs' Printed Circuit Handbook. And enough overview tables online, like this one preaching ENEPIG:
http://www.epectec.com/pcb/enepig-boards.html The main reason to like ENEPIG is that you can pronounce it like "and a pig" during conferences if you butcher it a bit.