Playing devil's advocate, the seated capacity of 150s and 156s are pretty much identical. Accurate figures are hard to find, and Wikipedia is not particularly reliable, but some PRM'd Northern 150s allegedly seat less than 130, compared to 140 or so on a 156. The marginally wider doorways of 150s are offset by an aisle that's generally too narrow to stand along. A 150 has the slight advantage of shortening the average distance between seat and door, but passengers are still having to shuffle on and off in single file.
With this in mind, I suspect that the 'wide doors' of many Mk3 DMUs and EMUs offer a bit less benefit than many assume. The vestibules on 150s, 319s and even 323s are only as wide as the doors themselves. Standing capacity is therefore modest, and the 'door area' isnt really wide enough for two passengers to enter/exit at once. It seems passenger flow can be improved by either employing wider doors (such as the class 185/350 etc), or widening the vestibule area (refurbished SWT 455s, and the Eversholt 321 demonstrator which freed up the deadlight zone behind the doors). The best designs do both, such as the cavernous vestibules found in 195s and 331s. They really do get people shifting.
Funnily enough, due to having only one toilet, a 4-car 331 (or 195) has about as many seats as a pair of 150s or 156s, even with all those tables! It's a pity that such an option is not on the horizon for weary travellers on the CLC.
If you could sacrifice a few seating rows on 150s, and widen the vestibule so it occupies all the space behind the door pockets, I think you'd see a noticeable improvement in loading/unloading times. However this would prove both costly and contentious. Failing that, I really struggle to see much difference in suitability between 150s and 156s on routes such as the CLC - even though the latter is much more 'civilised' to travel on, since you're not jostling for shoulder space on those crush-loaded runs.
But that's just my (somewhat over-articulated) stance.