Within $3 of each other, and neither includes a grinder — so this comparison comes down to boiler philosophy and portafilter standard, not price or features.
At $446 and $449, these two machines are priced within rounding error of each other, and neither bundles a grinder — budget for one separately either way. The real split is architecture: the Bambino Plus uses Breville's ThermoJet system, rated to heat in about 3 seconds, while the Classic Pro Evo uses a traditional single boiler that takes several minutes to warm up but is simpler and, per its decades-long track record, easier to service and modify.
Portafilter size is the other real difference: the Bambino Plus uses Breville's 54mm standard, while the Classic Pro Evo uses the 58mm commercial size, which opens up a much larger aftermarket of baskets and bottomless portafilters. That standard is a big part of why the Classic Pro Evo is one of the most widely modified home machines in the hobby.
The Bambino Plus, by a wide margin — Breville's ThermoJet is rated for a few seconds, while the Classic Pro Evo's traditional single boiler typically needs several minutes.
The Classic Pro Evo — its 58mm portafilter uses the same size as commercial café equipment, so third-party baskets, tampers and bottomless portafilters are widely available. The Bambino Plus's 54mm size has a smaller but still reasonable aftermarket.
No — both ship without a grinder. At this price point, that's standard across the catalog; budget for a separate grinder with either machine.