The Saints Row franchise is the closest competition to the behemoth that is the GTA franchise, with the difference between the two being the levels of realism. GTAIV was as close to a living, breathing, virtual city as you could get, but it suffered from being too real. SR3 on the other hand is zany, crazy, and at times as far from reality as you could go. Neither game is bad, but likewise neither really shine.
Gameplay wise, Saints Row 3 offers nothing really new from it's predecessor. Stillwater is now Steelport, and there are 3 different gangs to destroy, but the core gameplay remains unchanged which isn't a bad thing. SR3 does jazz up rewards however, with each level unlocking more rewards you have to pay for. This is good as it means infinite run is obtainable by doing anything, you don't have to do a certain activity to get it. You also get to upgrade weapons, making them more powerful and have different effects. The downside to this system is that if you spend a lot of time doing side activities you end up with enough cash to buy yourself perks and weapons to obtain almost godly status before even touching the main missions.
The storyline is fairly similar to SR2 too, with the Saints having to fight to control Stillwa, sorry Steelport against rival gangs. Musically nothing much has changed either, The Mix is still the only radio station worth listening too, with all the others featuring mostly lesser known artists with the odd big name thrown in.
What does set SR3 apart from it's predecessor is the sheer silliness it descends into. SMG's which set enemies on fire, space ships with laser guns, hacking via a motorbike in a Tron-like style and guns which fire sealife are all pushing the realms of plausibility. Gaming is escapism, but I like my gaming to be reflect the era on show, we may as well have the Saints take on a giant dragon, or sprout wings and fly. SR3 also takes the sexual content to new depraved heights, nudity is common place and the game spends lot of time in sex dens with bondage equipment strewn all over, you can even wield a giant rubber dildo as a weapon. Moderate usage of sexual imagery is tolerable, but SR3 seems to be trying to shock, so the effect is diminished.
As this is the full package you get lots of extra cosmetic and vehicle items, and 3 pieces of content DLC. Sadly all 3 pieces are lacking to the point that calling them content could be slanderous. Each one will take you roughly 45 minutes to complete, as you're almost god like by this point. I honestly spent longer flying around grabbing the collectables.
In short Saints Row 3 is pretty much more of the same you've come to expect from the series. It isn't quite as good as SR2, but it is still a fun little game which will while away a few hours.