To address the points raised by Mr. Levitator:
1. Speed: Duchess ~150-160kts. Baron typically 175 to 185. That's not really worth paying the extra for. Approach speed isn't significantly different. If you really want to think faster in the approach then fly the Duchess using Cat B approach speeds.
2. Systems:
How is the Baron more complicated? Fuel x-feed works the same way. Cont. IO-520s are injected but apart from hot starts & the Cont. fuel flow needle allowing an easy leaning facility there's no difference in operation. In fact the carburetted Lyc O-360s might require more technique due to carby ice considerations.
Both a/c have retractable gear. Big deal. Select up or down as required. Baron has a hand crank for emergency extension, Duchess needs a special tool (if your arms aren't long enough to reach the floor in front of your seat). Still not a significant difference.
Both a/c have single tanks / wing (ignoring any optional aux. that might be fitted to the Baron. No guarantee that the training a/c has them). If system complexity is such an overriding consideration go learn in a C310 with nacelle tanks.
Electrical system operation is arguably more complicated in the Duchess. It has a split avionics bus. Barons normally don't.
So....still not worth the extra $$$.
3. Weight/performance consideration: The Duchess is a 4 seater operated 2-up. The Baron is nominally a 6 seater operating 2-up ie a lesser proportion of it's full ability. That would leave a greater comparitive performance reserve for single engine ops. The lesser performance reserve of the Duchess is a 'good thing' for training.
Again........no advantage to the Baron.
4. Handling. The Duchess IS lighter than the Baron. No argument there. That means it's more subject to altitude/speed deviations from turbulance compared to the heavier Baron. I'd argue that's not necessarily a bad thing for a student trying to develop a good scan technique. Barons fly like they're on rails compared to a Duchess.
The Baron has a bit more inertia so & is capable of slightly more speed. Doesn't take more than a couple of hours to get used to so why waste your money using it through the whole course?
About the only argument I can see that would support using the Baron is one where a job is on the horizon that requires Baron experience.