Stronglifts and Starting Strength are both based on fairly solid scientific evidence, however, neither program as a whole has been properly scientifically evaluated. You can summarize each like this: "Take advantage of the novice effect and large compound lifts to allow incremental increases every workout for months."
The novice effect has been demonstrated in the literature: untrained individuals gain strength more quickly than any other group.
The usefulness of compound lifts in developing functional strength and allowing incremental increases is also fairly established. For example, squats have been shown to be well correlated with sprint times and vertical jump height.
Working out in the 5-rep regime (both programs advocate 5-rep sets) has also been shown to correlate with strength gains rather than hypertrophy (size) or endurance.
So, if you're a novice lifter (meaning that you can recover from your lifting your 5-rep max in about 2 days), and your goal is getting strong, both Stronglifts and Starting Strength should work for you. They're supported by research, and tons of empirical results.
Here are two articles that explain the reasoning behind these programs:
- httpStarting Strength://startingstrength.com/articles/novice_effect_rippetoe.pdf Novice Effect
- httpStarting Strength://startingstrength.com/articles/incremental_increases_rippetoe.pdf Incremental Increases
There is less scientific evidence for choosing Stronglifts over Starting Strength, or choosing Starting Strength over Stronglifts.
The differences are basically small details. Stronglifts uses 5 sets at the work weight, while Starting Strength uses 3 sets at the work weight. Starting Strength incorporates power cleans, but Stronglifts doesn't. Stronglifts says add at most 5lbs per lifting session. Starting Strength says add up 10-20lbs per session for the bigger lifts like deadlifts, at least at the start, when you're able to make quick gains in technique and strength. Starting Strength (the books) seems to have a more complete description of the program and techniques behind all of the lifts than Stronglifts provides.