Say you have a 128GB ssd device and a 256GB ssd device. Will the bigger storaged ssd device be faster than the other? In general, does more memory mean better speed?
So a few things here. First: SSDs are used for storage. They aren't memory. Having more memory CAN produce an increase in speed, but is not guaranteed to do so. Having an SSD replace a hard drive will considerably speed up a system.
As for what I THINK you meant to ask: "Does having a larger SSD result in a better speed?"
My observation is: Eh, kind of. From what I've experienced, larger SSDs usually have mostly similar speeds to their smaller counterparts (from the same manufacturer, etc.). However, there is a special case that I want to mention, which may contribute to the confusion: There exist some ssd-based flash drives, which absolutely DO have different write speeds based on what size you have. I believe this is due to the fact that multiple chips exist on the flash drive to increase its capacity. So, if the individual chip's write speed is the limiting factor, then giving more of them could increase the overall write speed of the USB bus.
My guess on why this isn't as much of a thing on regular SSDs is because of their physical size, they can handle physically larger chips, and/or additional circuitry that eliminates the need for lesser chips.
More storage isn't related to more speed. There are many aspects which contribute to the speed of a SSD, for instance there a SSDs where the storage structure differs in Single Level Cells (SLC) and Multi Level Cells (MLC). The SLCs are more reliable and faster. On the contrary they are more expensive. The controller of the SSD should be also taken into account, because he is responsible for processing the data. An important performance value to look at is are the Input/Output Operations Per Seconds (IOPS). If this value is high, you can be sure that your controller is valuable.