Favorite how? As a practical carry gun? As an interesting design? As best in fit and finish? As most original design? As most/least complex?
The Frommer Stop is a really interesting design, but I doubt I would carry one if a Walther PP or a Colt Pocket Model Hammerless was available. The Savage 1907, Remington 51, S&W 1924* and Davis-Warner are good examples of working around Browning patents, but at the cost of complexity.
*The 1913 is outside the criteria, being a .35 caliber.
Jim