Dave Tate describes progression in fitness (and indeed, anything) to go in 4 generic stages:
Starting Strength and StrongLifts 5x5 are both novice barbell programs built around major compound lifts with simple progression and a clear scheme to get you from shit to suck. The two programs are different but very similar, using most of the same exercises in a similar order, on a 3-day-a-week full-body rotation of two alternating workouts with linear progression. For some reason, the great similarities between the two programs seem to spark a lot of aggression online over the relatively minor differences, and thus the tyrade of arguments from people who, if they had the experience to warrant debating such topics would also have the experience to know that they're making mountains out of mollhills, commences.
Let's have a look at both programs.
Starting Strength by Mark Rippetoe with Lon Kilgore
Starting Strength is both a program and a book, which is now in its 3rd edition. I've only read the 1st and 2nd editions, so I'm not sure what modifications have been made in the latest edition, although I've heard that there's now a change in technique to the press, and the addition of pull ups after a couple weeks in the 3rd edition. If you've got a copy of the 3rd edition, you can correct me on that, or give further details, if you feel so inclined. But here's the program as of 2nd edition:
Bench Press 3x5
Power Clean 5x3
You train a total of 3 days per week, adding weight to the working sets every session, so long as you got all your target reps with good form. The first time you perform each lift, with the help of a coach, you'll begin with the empty barbell for sets of 5 and add weight until you find your initial working weight, which is whenever the bar speed slows or it looks like any further weight increases will cause technique to break down. This might mean squatting 50kg, benching 40kg and deadlifting 60kg on your first session (just random numbers, don't treat these numbers as a recommendation). You'll also add weight each session according to how much you can safely progress by. For a lot of people, this means adding 5kg/session onto squats for the first fortnight, and up to 10kg/session onto deadlifts for the same period. As you get stronger and more skilled at the lifts, your ability to progress will decrease, and so 5kg jumps will become 2.5kg jumps, and 2.5kg jumps will become 1kg jumps (if possible -- you'll need smaller plates than most gyms provide to do this), etc. Eventually, you'll start missing reps. That means, you might be aiming for the prescribed 3x5, but instead only get 5/4/3 or 4/4/4 or some other combination that isn't 5/5/5. If this happens, you won't add any weight in the next session. Instead, you'll use the same weight, trying to get the extra reps. If you fail to get all your reps 3 sessions in a row, you'll decrease the weight by 10% and work back up. Once you've stalled and deloaded 2-3 times on the squat, it's probably time to move onto more advanced programming.
StrongLifts 5x5 by Mehdi
The first thing you'll notice about the StrongLifts 5x5 report, in contrast to the Starting Strength books, is that it's free. Unfortunately, the saying "you get what you pay for" rings with an element of truth here, as a great volume of the report is Mehdi selling his system, rather than teaching you how to lift. In contrast, in Starting Strength, Rippetoe goes to great lengths to talk about the individual lifts -- what muscles they develop, how to do them, common errors with corrections, how to warm up and even trivia about the lifts (all with a lot of photos and diagrams so that you can literally see what he's talking about). The StrongLifts 5x5 report gives less instruction and more sales. But, that's the e-book. Let's look at the actual program.
Bench Press 5x5
Unlike Starting Strength, StrongLifts does not involve the lifter spending time on the first session ramping up the weights to figure out a starting weight. Instead, the starting weight is purely and simply as little as the lifter can get away with. This means the empty barbell (20kg/45lb) for squats, bench press and press, and slightly more on the row and deadlift (officially 65lb and 95lb respectively, which is roughly 30kg and 40kg...personally I'd go lighter on the rows, especially if you have access to super-light 45cm plates at 2.5kg and 5kg, however most healthy young males probably won't have any problems with the 40kg deadlift, assuming they can learn appropriate technique). So, the starting weights are usually going to be lighter than in Starting Strength. The progression is also slower on StrongLifts 5x5, adding just 2.5kg/workout from day 1, with the goal of hitting a 225lb squat for 5x5 after 12 weeks. The working sets for squats, bench press and press are all 5x5 instead of 3x5, so there's an extra 2 sets in there, and 5x3 power cleans are replaced with 5x5 rows.
So then, which is better?
Frankly, it's an either/or situation. There are pros and cons to both these programs. Personally, I don't think either of them has enough upper back work to balance out all the bench pressing and overhead pressing, although the 5x5 rows rows of StrongLifts will do more to balance out the pushing than any amount of power cleans ever will. If you want to be good at power cleans, obviously a program that actually includes them will be better for that purpose than one that doesn't. When you're starting out, you want to do as many good reps as possible without wrecking yourself. I think doing 25 working reps (5x5) of most exercises at far too light a weight provides that potential more than 15 total working reps (3x5), however Starting Strength allows you to potentially start with heavier weights and progress more rapidly. It's also easier to recover from only 3 working sets than from 5, given an equal load, so once you've learned technique, Starting Strength may become preferable over StrongLifts 5x5. Instruction-wise, the Starting Strength books trump the StrongLifts resources many times over, in my opinion. Starting Strength provides one whole chapter per each of its 5 lifts. StrongLifts 5x5 only offers links at the back of the report to 1-pagers on the 5 lifts. Basically, if I were training a rank novice who doesn't need to have power cleans (or an equivalent movement) in their program, I'd prefer to start them on something like StrongLifts 5x5 but with the coaching of Starting Strength, and then back off the volume when the weights get hard (to something that more closely resembles Starting Strength, anyway). If I were training someone who needs to learn power cleans, I'm not sure I'd put them on Starting Strength for it, unless they're something like a rugby player. No matter who the person is, if I were training them they'd have more upper body pulling relative to upper body pushing than either of these programs provide, because I like people to not have dodgy shoulders. Whatever the case, both of these programs are for beginners to learn basic lifts on, and if you're a beginner, you just have to show up and consistently go through the motions in order to get results, so, as I indicated earlier on, getting into a heated argument over this is just plain silliness.