It appears that the Bridgeport is an older M series (round ram) machine. As such it's probably only 1 hp at best (most likely 1/2 hp) and can only use collets up to 1/2". The collets are either a B-2, MT#2 or B&S #7. None are as common as the R8 collets used in the newer series I machines. R8 collets are available up to 1". However, it's recommended to stay in the 3/4" to 7/8" range. 1" collets are very thin and not very strong. The M series machine has a quill travel of 3 1/2". The series I machines have a quill travel of 5". This machine weighs in at about 1,500 lbs.
If the Lagun is in good shape it's the better choice. It has the much sturdier (and easier to tram) V ram. They come in several versions, but are usually 2-3 hp or more. They most commonly use R8 collets, but occasionally are ordered with different spindle configurations. This machine weighs in at about 3,100 lbs.
Keep in mind these recommendations are made from the limited pictures and without having any knowledge as to the conditions of either machine. I have a 1 1/2 hp Bridgeport Series I machine with the variable speed head. It's more than adequate for the work I do. At the time I was looking there were a few Laguns on the market, but they were beyond my budget. My first choice at the time was a Tree brand mill since they were the ones we used in most of our machine shops. There were very few available and the prices were well beyond what I could spend. Several of the people I worked with had run Laguns for previous employers and thought they were excellent machines.