I am going to assume you're running in the same windowed resolution as you would be fullscreen (i.e. if you run it in 800x600 windowed, you're comparing against 800x600 fullscreen), since that means the game has to render the same image in either case. If you run in a higher resolution for fullscreen, then it seems likely that there's something else going on.
When in windowed mode, your computer has to draw more than the game itself: your desktop and other windows are also visible, and time has to be spent on drawing that as well.
However, there is another, more subtle difference, which your games may or may not make use of - it was somewhat common in previous years, but I'm not sure if game companies are still using it.
You see, the image you see on the screen is nothing more than a contiguous collection of rows of pixels. That is, nothing is stored between each row of pixels: it's just one large chunk of memory.
In fullscreen mode, the game can just place its image in that chunk of memory; when one row ends, the next begins, so you can copy your entire rendering buffer in one go. In windowed mode, that doesn't work any more: you now have to copy each row individually, because you have stuff to the left and to the right of your window which you aren't allowed to overwrite.
If your hardware is sufficiently fast, the difference should not be noticable, because although it is more work, it is not really that much more work - not as long as you aren't keeping a ton of other things with complex rendering visible at the same time - and if you're capable of getting the full X FPS in fullscreen (where X is your monitor refresh rate), it's quite likely that you could also get a few more FPS, and the computing power that could have been used for those extra FPS, can instead go to all of the other stuff happening in windowed mode.
To answer your question: no. Not a "good" way. Borderless mode, or Fullscreen Windowed mode as you call it, will fun the game as "fullscreen", though as a borderless window application. said window is not re-sizable. An adequate solution would be to open a completely black picture to have underneath a regularly windowed game, and set the resolution on said game lower. You will have the border from the game, and you'll have to open a picture every time you wanna game though (plus, it's another thing to have to keep in front of your browser and such after browsing something).
Personally, I have yet to play a game that allows resizing of the rendered area in the game window at all, much less re-sizable borderless windows.
Best Answer
With windows 8 and above, the OS can detect when a game is running in borderless windowed mode and give it exclusive GPU access, which means there is no performance penalty. This only works if it is using the full screen, so if you have other things on top (volume indicator/notifications/etc) then it will fall back to normal windowed rendering until the notifications go away.
TLDR; The performance penalties of borderless fullscreen no longer apply in Windows 8+, with the possible exception of with multi-gpu or multi-screen setups.