The class 319s have 990kW at the wheels of the four driven axles in a four-car unit. In an equivalent four car consist of two two-car class 150 DMUs, there is a combined power of 852kW from the output shafts the four engines* that drives half of the axles. Simplistically, that's 86% of the 319's power. However as you mention, there are several factors that need to be considered when assessing the power at the wheels.
For the class 150s:
The maximum power is only available from the engines at around 2000rpm and is an absolute peak determined by the engines design.
The maximum power figure of the engines is for those in perfect operating condition, probably just released from overhaul.
The power at the wheels is subject to considerable loss in the torque converters especially at lower input shaft speeds.
For the class 319s:
The rated power is a continuous rating determined by the motor and transformer design including thermal regulation.
Electric traction motors and transformers have short term peak ratings (higher than the continuous figures) that can be called upon to deliver short periods of higher performance. This is especially true for the motors, some of which may have to compensate for faulty motors that have been temporarily disconnected.
On ac, the 319s probably nearly always had full power available to them. On DC, they would be susceptible to a lower peak output when the nominal 750V 3rd rail fell to lower voltages, (not uncommon on a busy DC route or at the end of a long section fed from one end only). Either way, the difference is unlikely to make much difference when poor railhead conditions are present.
As far as adhesion is concerned, the class 150s had an axle load of 9.375t on the driven wheels whereas the class 319s had a load of 12.65t so the difference in adhesion is not as much as the 50% vs 25% proportion of driven axles might suggest. I believe that the 319s have automatic sander and wheelslip detection but I can't comment on whether the 150s do. All of that probably accounts for the drivers having gained plenty of experience with the trains through three(?) winters can now mitigate any shortfalls in adhesion in the same way that the Thameslink drivers did. Even ignoring the switchback gradients in the core, I don't think that the NW lines are significantly worse than the MML and BML routes on which they have been running for years.