What ram?

Use Crucial's tool to correctly identify the required modules, then you can either go with them, or buy elsewhere. I have always found them to be top notch, and you get a lifetime warranty. Don't be tempted to buy so called "Value" RAM though:


http://www.crucial.com/uk/store/dra...le_uk&ef_id=UhBteQAABfnmIjmK:20130818064513:s

 

Likely 1066 vs 1333 speeds..

Yup.. as mentioned, the Crucial site works well I believe, and I have had NO issues ever with this site either, and it always has truthfully given me the MAX Ram numbers, even if APPLE has stated a smaller amount..

I believe your 2010 15" MBP likely has 1066 MHz PC3-8500 DDR3 SDRAM and a if the 2011 13" MBP is 1333 MHz PC3-10600 DDR3 SDRAM as it appears, that will be the issue.. same amount of pins and may fit the socket, but computer will not recognize likely..

You can find almost ANY Apple Product on this site, MBPs are listed here:
http://www.everymac.com/systems/apple/macbook_pro/index-macbookpro.html

 

The MBPs with NVidia chipsets (including the 13" mid-2010s, and mid-2009 models sold in 2010) are very finicky with RAM speeds. You will generally need to run 1067MHz DDR3 speeds, rather than faster speeds (some people have reported success using faster speeds, but as you've found, there's no guarantee it'll work).

Later MBPs with Intel chipsets are not picky and will happily run faster speeds...