Yes, BGA do require tight process control, but they are extremely consistent. Lead-free BGA in its infancy years ago wasn't too great but things have vastly improved since then.
If you need even more reliability you might look into underfills. It will help prevent the package from shearing off, but again in most applications where you'd have enough G forces to warrant this, there will be bigger components with even more susceptibility.
For vibration and shock reasons you may want to go to solder-mask defined BGA pads, and tighter specs. This is the alternative to the more common NSMD (non soldermask defined). The larger area of copper on the pad makes shearing less likely.
Also you probably know this, but RoHS has exemptions for certain categories of products, such as automotive, test and measurement, aerospace, military, etc. where lead is allowed.
For long term longevity lead provides a significant advantage as the presence of lead in solder largely prevents tin whiskering.
There is still research being done on the longevity of devices with leadfree joints in adverse conditions. Whiskering can happen at random, but is exacerbated by excess shock (both mechanical and temperature). Toyota and BMW have had problems with this (fly by wire pedal sensor pots having whiskers causing reliability failures, entire ECUs failing from whiskering)
Some vendors selling parts in BGA packages will provide both leaded and lead-free preballed packages. But as a whole, things are pretty much all leadfree now anymore.
And like a previous poster said - with regards to placement BGAs are far more forgiving than QFPs. I had to do some rework on a 208pinner and would've preferred reballing a BGA instead. I have placed and reflowed 0.8mm pitch bga myself at home and had no problems.
BGAs will require more pcb layers to fanout all their connections generally. It depends a lot on how many connections you need to break out, signal types (single ended, SSTL, voltage references, LVDS blah blah) but you can do up to 256balls on 4 layers, 484balls on 6 layers, 780 on 8 layers, etc. However, the overall pcb size can be greatly reduced with BGA vs the same part in QFP.
And since QFPs larger than 300 pins rarely exist (and you dont' see QFPs bigger than 200 pins really anymore) it is worth dealing with at some point.