Hey there!
With Sweet Spot and Threshold work, mid-interval stopping has a big negative impact on the effectiveness of the workout, so I would recommend sticking to the trainer if you don’t have time to make it out to the hills.
Regarding climbing vs. flats, you will recruit slightly different muscles due to the incline. Your power application will also feel slightly different due to the reduced inertia associated with the lower speeds seen while climbing. However, these are relatively minor and you can still get a great and effective workout by hitting these climbs.
In general, it is a lot tougher to execute your rides outdoors, especially for rides like Spanish Needle, Over-Unders, or anything where a high level of precision is required for successful completion of the workout. Typically, we recommend the highly structured work to be completed on the trainer, while the less structured work like Sweet Spot and Endurance riding can take place outside, provided you have the roads for it.
This thread could also have some food for thought 