I have had experience with several braille displays. I will review these below. Please note that I have not had experience with many popular braille displays, so you can't be sure of finding a specific one in this list. If you want to learn more about a braille display, you can find the websites of the company that makes it and its specific product page above in the table.
The braille displays are organized alphabetically. Each review is listed under a level three heading to facilitate navigation.
This is a great concept that doesn't work in practice. This very expensive display does have most of the typical functions, but runs these in a very complicated manor. All actions are controlled by the menu, which is poorly organized and extremely long. The drivers that run the display can easily fail, causing the display to randomly disconnect. It also allows for the purchase of a "feature pack" which allows for braille input and sound output via the display. The braille input works as long as the display does (which is only sometimes), but the speakers are mis-oriented so directional audio is reversed. In short, I would not be able to recommend this display to students or professionals.
APH Refreshabraille 18
This is the smallest display with which I have had experience. It is very nice for most things; its bluetooth and USB connection are basically flawless and its settings menu is nicely laid out and easy to understand. There are only two negative aspects of note with this device. The first one is that the USB port is set into a slot on the bottom of the device. This does an excellent job of keeping the port safe, but causes problems when one attempts to insert the USB chord for charging or connection. This can take longer than can USB connections to other displays because it can be tricky to align the cable and port. The second problem will probably not occur to most users, but the display can come apart if the coverings to the cells are gently pried. If this occurs, the pins that form the braille cell will almost certainly fall out and become lost. To protect yourself, simply avoid situations in which the outer casing of the display would be pried. I can recommend this display as a comparatively inexpensive display, especially for use with mobile phones.
Freedom Scientific Focus 40 Blue first generation
Note that this display is no longer being manufactured or sold by Freedom Scientific. However, there are many secondhand sources for this generation. This article does not apply to the second or third generation of focus displays.
This display is nicely designed and easy to use. I have successfully used the display with NVDA, VoiceOver for OSX, VoiceOver for IOS, and JAWS for windows. The drivers are a simple installation away, and connection takes seconds if not automatic. The display does nothing on its own, but does offer a keyboard for convenient text entry. The keys are relatively quiet for text entry. There are several keys on the front for navigation in text, and the display also offers Freedom Scientific's handy whiz wheels for easier navigation.
Freedom Scientific PacMate Braille Display
This display is designed to connect to the PACMate from freedom scientific, but if disconnected from this device, it can be connected to a computer. However, this means that it has few features. It lacks both a keyboard for text entry and a bluetooth radio. Therefore, it is not compatible with mobile devices. It does offer freedom scientific's whiz wheels for easy navigation and cursor routing buttons. The price for this display is about equal to similarly-sized displays with more features, so I could not recommend this display as a cost-effective device.
HandyTech ActiveBraille 40
The activeBraille 40 contains a few of the features of a dedicated note taker. You can write documents to store them on the device for later viewing, manage appointments, and even work with a small subset of the music braille code. The cells of the display know when you are reading over them. This enables the display to do interesting things such as auto-advance when your fingers are close to the end of the line. Unfortunately, this has not been fully implemented by readers that support this device, and the cells result in a price nearly double that of displays of a similar length. Also, the cable used to connect the activeBraille via USB does not use the mini USB connectors that connect all of the others described here. I believe that the ATC technology will be very beneficial in the future, but it is simply not valuable enough to justify the high price tag.
Hims Braille Edge 40
The Braille Edge offers a small notepad for reading and editing files stored on an SD card. This means that it can be used even if the computer or cell phone it is typically connected to is not present or has run out of battery. There are a few other applications available, including a clock with alarm and stopwatch, a scheduler, and a calculator. It does not have the full functions of a notetaker, however, so it provides a nice medium between the two options. Connecting the device is very easy. The bluetooth and USB connections take essentially no time at all, and the device even offers a convenient switch to toggle the mode of connection. There are extra buttons for using the display with windows, but in my experience the buttons are more useful for setting up custom commands, which can be programmed into NVDA or VoiceOver (OSX only). I would recommend this display for most tasks as the best combination of features and price I have seen to date.