2011 machine can hold up to 16GB of RAM, 2-8GB sticks.
It's almost 2014 now, that's about 3 years. OS X Lions need 4GB+ easily, programs are being bloated.
If the machine was heavily used, the keyboard and trackpad worn, or if it's a 13", then go for the third party 8GB and stick it in yourself and make do.
If it's a 15" or 17" and not heavily used, or if your needs will exceed 8GB RAM, or it has a SSD already, and you have been babying the heck out of it, then perhaps the $300 is worth it.
Average lifespan of a laptop is about 3-4 years, more with considerable care and wear and tear placed on external devices.
So it's nearly 3 down now and X amount to go, depending how well you treated and took care of it if it's worth spending $300 for another 3 years or not.
You can always try the 8GB and likely that will be enough, or if it doesn't work, return the RAM or sell it on eBay and get a new machine (newer machines need newer RAM specs usually, but not in all cases)
My Early 2011 is like brand new almost, it still has the factory smell a little.
The keyboard perhaps had 100 characters typed, it's covered by the thin foam packaging and the trackpad wasn't used at all hardly. Superdrive was only used a few times.
My machine with your problem would make a ideal candidate for a $300 fix, as it's the last 17" Apple made and still kicks arse so it's worth a lot used still as people want it for Snow Leopard and it can be upgraded to 10.9+
But if yours is a 13" well that's a less powerful machine, no dedicated graphics and it's hot, so it's not worth as much for a $300 repair as it's closer to the 3 year lifespan and obsolence than a 15" or 17" 2011 model.