I think it stems from the initial directions each co took.
MIPS started from a 32bit Stanford grad project (MIPS-X) spun out to become the R2000 workstation class CPU. No hint of embedded arch at all at that time.
They steamed on finally hitting 64bit archs relatively quickly. Once they got to the R4K32 series and upon adding MIPS-16, they had a small footprint embedded soln but...
ARM started from basically a hobbyist computer, already with some small footprint pedigree built in. Very quickly Thumb was adopted, arch just as a translator initially but subsequently with on chip native decode. Now they have a 64bit arch, but because of their small footprint roots and aggressive licensing, they
really caught the lions share of sockets. They can now come to capture a 64bit space that was MIPS's to own years ago by osmosis of the socket market.
ARM had a first mover advantage in embedded and they executed well and did not allow competition to unseat them. It could have been different, they could have mucked up a design and lost share, but that did not happen.
Both companies have first rate tool chains also (that can be a deal killer). Thus its a wash for softies when HW pitches a design, if the license is favorable, and the die area+power draw meets managements expectations, then that vendor will get the nod for new IP. ARM has been fortunate in that there is also a bit of industry simpatico wrt ARM adoption... others are using it, so why not us?