In terms of horsepower and engine options there were no differences between the two tractors. The difference was how the tractor was physically configured.
135's are utility tractors with a lower center of gravity and could be bought in the US as Narrow, Orchard, Vineyard, Special (Barebones w/z134 engine), and Deluxe. They had a lighter front end which typically made them less suitable for loader work. Engines were the Perkins AG3.152. AD3.152, Continental z145 and z134.
150's were the "row crop" version of the 135 sharing more design elements and components from the 165. In other words, the 150 was a taller profile tractor and more than likely be available in a Standard, high-arch, tricycle or single wheel configuration.
If I recall correctly they did not have the control beam set up on the three point that 165 and the 135 Orchards came with. Engines that were available were the Continental z145, Perkins Gas and Diesel. MF 150s typically came with Flat top fenders whereas on a MF 135 it was an option. The pressure control hitch was an option on both series (minus the 135 Special).
The 150 was exclusive to the US (and maybe Canada) . The 135/150 would compete against the Ford 3000 AP and the John Deere 1010 in its various configurations. Horsepower was approximately 38-
42HP and this tractor would have been a three (bottom) tractor. MF Poor has a beautifully restored MF 150 he bought new.