It's apples and oranges here. I will try and explain for the non-technical if I can.
All of the emulators you run on your PC and other devices are software emulators. They try and reproduce the behavior and interaction between everything entirely via software. It's a big program trying to do the job of many components and tie in your device's input and output. They are subject to lag no matter how well designed because many things in software can't happen in parallel, input and output translation takes time, and your video and audio is subject to constraints like APIs, drivers, OS, monitor refresh rates, etc. The environment is totally different from the original system. There is a lot of translation going on to bridge your PC or device to the emulated behavior of the SNES even in the best emulator.
An FPGA (field programmable gate array) is basically an integrated circuit containing banks of electronics and programmable pathways. Even though it's 'programmable', it's really just setting up a description of how the electronics are configured/connected. That subsequently dictates what the electronics will end up doing. Hence, they are 'programmed' (configured) with a special hardware description language (HDL) rather than a software language. FPGAs are not processors. So, you can set up the banks of electronics to connect and function in a certain way. There is no software executing. It's all real time-time electronic component execution. Things can execute in parallel in real-time like the original electronics, and there is no lag to speak of. There is no input or output translation going on (some notable exceptions exist like hardware HDMI out). The circuits can be set up to mimic the original SNES board. It can take the same inputs and output the same signals. It's a bit simpler in overall design compared to an emulator because of this. Until recently, FPGAs that were large enough and fast enough to handle the complexities of the SNES hardware did not exist or were not cost effective. That is why these types of products didn't show up until more recently.
With that said, they are both subject to the same type of behavioral flaws. Both emulators and FPGA designs must be based on reverse engineered information of the SNES. If this information is not 100% accurate, you will have flaws running games on your emulator or FPGA. The difference is emulators are implementing behavior in software at all levels, while the FPGA is implementing behavior only at hardware block and/or signal level.
In theory, it may be easier to get 1:1 behavior using the FPGA design over an emulator because you have much less you need to deal with, and you can directly compare electronics operation and signals with an original SNES board side by side. In the ideal world, an ideal emulator and ideal FPGA design would show no difference other than lag though. However, we don't live in an ideal world, nothing is perfect, and you will need to be the judge! Maybe you'll like the apple, or maybe you'll like the orange, but both are good SNES fruits to have!
I hope this helped and didn't further confuse you!