Everyone who has searched for programs on the internet have run into some form of a 5x5 program and tried it out. Many times these routines and rep ranges are seen by a lot of individuals as something aimed at beginners. Let's dig a little deeper into what a 5x5 range does compared to other rep ranges that total close to the same amount of volume as a 5x5. 
For many people a 5x5 approach is a good middle ground and that's why to my understanding why Starting Strength has chosen to work with 3x5 and 5x5. With faahve reps we are at the sweet spot where we train a good amount of strength and also do a decent amount of damage to a muscle so it can grow after it has recovered. I think programming a movement to a rep range of 5 is great in any program that works towards GPP (general physical preparedness) for most people. You can load up to a decent % out of your 1RM (repetition maximum) to stimulate both your nervous system and your muscles, so that moving to either a hypertrophy or strength phase will be smooth. To me this is also the beauty of introducing people to strength training via a 5x5 routine as it is a tested method to prepare an individual for future training regardless of their long term goals.
While 5x5 is great for GPP for intermediates and advanced lifters, I believe a 3x8 approach is much better to amp up volume. I don't find too much difference in the amount of weight someone can lift between 5 and 8 reps, unless the weight used is a true 5RM. We can build much more relative intensity into the workout by doing a 3x8, while keeping almost the same volume. For example when training for strength I've found it's better and more time efficient to work up to a bigger lift say 85%~90% 1RM for 3 reps and then add a little extra volume if needed with a 3x8 with 65%~75% 1RM than a 5x5 with the same intensity. If we were only going to do either 3x8 or 5x5 at the same intensity without any prior working sets, I'd definitely recommend a 5x5 as in my opinion it allows for a fuller workout by allowing for more effort output from the lifter.
That bring us to 8x3, if we wanted more effort output from the lifter it could be better to work on explosiveness and speed with shorter reps taking we are still working around 65%-85%1RM. An 8x3 is flexible in that sense that it allows the lifter to work higher volume at a higher intensity, so taking we are working at a strength phase why not go with an 8x3 at 85%-95% 1RM rather than a sole 5x5 at a lower percentage. We would be hitting the same volume, but with a higher intensity allowing us to focus more on strength. 
Here lies the difference of using 5x5 as a strength builder vs a GPP routine. During GPP we may not want or need to reach higher intensities, but we can have more sets with not as much perceived muscle fatigue as with 3x8. While 3x8 is great for adding volume into on-going routines, it wouldn't be that great as a standalone range. 8x3 on the other hand allows for great flexibility with intensity for the same volume being great for strength focused phases allowing for more specialization.
Examples
[General] 5x5 ----> 3x8 ----> 8x3 [Specific]
5x5 Leg routine for strength/GPP
5x5 Squats
3x 25ft Walking lunges
Tabata Hill Sprints
3x8 Applied Leg routine for strength
1x3 Squats 85%1RM
3x8 Squats 70%1RM //(Alternatively 5x5 70%1RM)
3x 25ft Walking lunges
8x3 Leg routine for strength
8x3 85%1RM
3x 25ft Walking lunges
Thank you for reading!
Which one do you use or are going to implement in future routines?
Keep on being strong & decentralized!
-Strongerest