If you're not using a lot of programs (Especially if your RAM usage was consistently below 50% when you had 4 GB installed) then you're not going to see a speed increase having more RAM.
The only way RAM provides any sort of tangible speed benefit is if your OS is constantly having to page apps from RAM to the HD in the pagefile b/c you keep running out of RAM. That is what causes the typical slowdown, b/c the HD is usually the bottleneck in a system, particularly mechanical hard drive.s In today's age of SSDs, however, that gap is slowly closing.
If your old 4GB based system did not page a lot to the HD, then having more RAM only means you have more free now than before. If you have an SSD where your pagefile is located (normally not, if you set it up the way is recommended) then it's not going to be very advantageous other than for the time required to remove items out of memory and to the SSD and then back again as they get called up for use.
If you do not have an SSD then the paging becomes much more time intensive, and becomes more noticeable.