Probably not at the same rate but close. In a down market, studios perform better than higher priced houses, but in up market, it is the reverse. If you can afford a bigger house, always go for it. It may sound like a stretch, but it is not.
Generally speaking the answer is yes. The only reason it wouldn't is if the market for studios veered away from the market for 1 bedrooms. Because generally studios and 1 bedrooms are sold to the same type of buyer they should follow one another, especially in the same building. Another scenario where the values might diverge is if one apartment had a view or some amenitiy that the other did not. The value of this amenity could change at a different rate than that of the basic living area.