I wonder if the statement might be a misquote of a more quantitative one: MOSFETs surpass BJTs, in terms of number of transistors produced. A change which occurred, what, back in the 70s, early 80s?
Back in the 70s, 7400 and LS TTL were still king for medium-high speed, board-level logic, and computing (and also ECL for the highest speeds). Meanwhile, MOS ranging from metal-gate CD4000 family, to NMOS and CMOS VLSI, took off massively, and never turned back. (VLSI = Very Large Scale Integration, thousands of transistors per die.) A single 8080 probably contains as many MOSFETs as a large card of 7400 (SSI scale) gates?
BJTs were never able to integrate quite as well, whether due to heat dissipation (that card of TTL would dissipate a couple ten watts, easily) or, Idunno, signal quality issues and design complexity? (There was an Integrated Injection Logic, which uses open-collector outputs fanning in to current-sourced inputs; it's completely upside-down to design with, because there's only fan-in, no fan-out to speak of. Signal levels are around a Vbe, so, would be quite sensitive to noise by itself.)
BJTs have been displaced in analog and mixed-signal spaces, too. I'm... not sure offhand what would be an example "breakthrough" shift to MOS, but there are lots of op-amps and such, mostly in lower voltage families, where mature CMOS (feature size ~200nm) dominates in affordable performance: higher bandwidth per supply current, greater functionality and integration (not just rail-to-rail inputs and outputs, but feed-forward techniques, precision auto-zero and chopper types), etc. (The feature size is relevant for two reasons: one, it's cheap of course; but two, it also performs better than bleeding-edge processes do. That's right, the transistors in a modern CPU actually perform worse, pound for pound so to speak; they're just so much smaller that they can get away with much higher frequencies (but not proportionally higher!) and much higher integration density.)
Commodity RF applications have been monolithic for some time. These are mixed-signal designs, including DSPs and high speed ADCs/DACs, as well as analog processing (filtering, mixing, PLLs, amps, etc.). They even use integrated inductors and transformers, in the higher frequency parts (>1GHz) -- crummy ones, but good enough to be useful! And these are all MOS, as far as I know.
Even so, there are some newer applications of BJTs, or similar devices anyway. Many fabs use a SiGe process for advanced op-amps. These devices have even better transconductance and capacitance, allowing even higher bandwidth per supply current, without sacrificing the input noise that CMOS tends to have, nor being restricted to low voltages.
Huh, I seemed to recall SiGe ICs were kind of an oddball or new thing, about a decade ago. Checking press releases, it looks like at least TI, LT and ADI (this was before the latter two merged) introduced parts with this process in 2006-2010. So it looks to be just another quiet innovation these days; you might never realize your op-amp contains germanium!
Tim