A Bloodrager is basically a barbarian who trades his rage powers for a bunch of useless crap and a fairly crappy spell list. There might be a gem or two hidden in there, but if there is, I missed it. You're probably better off as a straight barbarian for smashing stuff.
A Sorcerer is a spontaneous caster who gets spells one level later than a wizard, and whose only advantage - bloodline powers - is often gained in min/max builds by 'dipping' a 1st level of sorcerer and then going Wizard. For all that, they are still incredibly powerful especially if built to a theme and with bloodline powers that improve that theme (such as a Crossblooded Orc/Draconic Sorcerer slinging Fire spells, or a Sylvan/Elf or whatever the ones that improve save DCs slinging around Suggestion and Charm Person).
In this case, the advantage of taking a level of sorcerer is that you haven't taken more levels of the crappy Bloodrager class. An even better option is to retrain Bloodrager into Sorcerer entirely. Bloodrager gets a lot of abilities, but they are along the lines of '+2 to save DCs vs something that comes up once per campaign!' so overall much less useful than a Rage power that gives you a bite attack you'll use pretty much every single rage round as a secondary natural attack, or Pounce that you'll use every time you charge, or half CHA to AC that you'll use every time something attacks you.
If Bloodrager wasn't so intensely terrible, and this was, for example, a question about multiclassing Sorcerer and Barbarian in roughly equal measure (as the title implies), i'd advise not doing so. Without a focused plan and a higher level of optimization than the other characters in the group, Pathfinder's classes tend to screw over people who try to multiclass in that manner. 3.5's answer to caster/noncaster multiclassing, classes that granted dual advancement, are much more absent in PF. Eldritch Knight still exists, and a few others, but they mostly offer only half-advancement at best. PF's design attempts to enforce single-classing in general, with classes like Summoner, Alchemist, and Magus to fill the holes left by penalizing multiclassing. The 'hybrid' classes are a grab bag of weirdness rather than, as you might imagine, an alternative to multiclassing. Some, like the Investigator, look playable, but almost by accident.