The answer is yes. Also, using them at the same time may be necessary in order to be able to run certain programs.
All three are in fact based on Wine.
Playonlinux installs wine whether this is already installed or not. In fact, one of its most interesting features is that it can install and use different versions of wine for different programs and program versions, and in this way cope with version regressions. The corresponding Wine program is automatically downloaded and used, or it can be selected by the user who knows what he's doing. Playonlinux also installs Winetricks to run wine scripts.
Wine installs in
~/.wine. Playonlinux installs in
~/.PlayOnLinux/wineprefix/. But running wine from menus after it was installed by playonlinux would create the
~/.wine folder. From this point of view using Playonlinux already involves in a way using Wine as a separate program. There is no point really in installing Wine after installing playonlinux. Playonlinux installs Wine, which then can be then used from playonlinux or separately.
For example, I have installed ImgBurn in Playonlinux, but then went to menus, wine, and installed foobar2000 there just to test and this player now is available from wine but not from playonlinux. But programs like Foobar2000 and ImgBurn are easily installed in all of the three options. Others, like msoffice, especially older versions, are a different matter.
Playonlinux is a GUI, but also a program with supplementary specific features. It seems made for games, but I cannot tell whether it is really better then crossover, for example, in dealing with games.
Crossover has impressed me greatly, but it still may lack some features offered by playonlinux, so having both makes sense. The big advantage with crossover is in the way it facilitates the installation of programs that are difficult to put to work in Wine and playonlinux, like older versions of msoffice. It installs in
~/.cxoffice. I have not tested it enough but I believe it to be indeed a superior program. (While I was not able to install msofficexp in the other two, in Crossover it was very easy to do.)
For many small programs it makes little sense having all these three programs at the same time. But for certain special cases like msoffice (which i tested) or games (which i didn't test), and I guess for bigger and complex programs in general crossover and playonlinux may be necessary, so that one could be .
After you test them please report here your conclusions.
Update: I was able to install Kindle for PC in Crossover, but it would not run. In Playonlinux, Kindle for PC is registered in the list of software that can be selected for installation; after selecting it, a specific Wine version 1.4 was installed and the application was able to run. This is a good example how PlayOnLinux is very necessary.