Hopefully it's a good competitor to these (people tell me so), but I hadn't used them before embarking on Veusz! I mainly got annoyed with the state of command-line plotting facilities in astronomy and unix (like IDL, gnuplot, etc).
I started with the idea that graphs should be built in an object-oriented fashion out of widgets. The widgets are arranged in a tree, a page holds a graph or a grid of graphs and a graph has axes and plotting widgets, and so on. Each widget has a set of properties and formatting settings which can be changed. It's now gained more data manipulation abilities. Data is stored in named datasets, linked to external files or entered manually, or you can even capture it from sockets or external programs. You can easily write a plugin to load your own file format. There are a set of data manipulation plugins for filtering and so on (again you can write your own). When plotting, you can just enter expressions to investigate your data.
Most of Veusz is written in Python with PyQt. There's a bit of C++ code to handle the inner loops, but it's pretty responsive. The next release should support Python 3, too.
One nice thing is that the saved files are simply python commands to regenerate the plot, so it's easy for the user to automate making plots. You can also use it as a python module for plotting, using the same command interface as the saved plots use.
Veusz is nicely designed and quite original. There are a few Qt-based programs more similar Origin: QtiPlot, LabPlot, SciDAVis. In 2009 there was a big announcement, featured on LWN and other Linux websites, that LabPlot and SciDAVis (QtiPlot fork) will merge, but soon after both projects died.
At that time QtiPlot was very actively developed by one guy who was living off license fees on his GPL'ed program. I was trying similar thing then (with program called fityk) and emailed him to ask how is he doing. In my case, it was interesting experience but after a few months and depleted savings I had to find a day job. He survived much longer with more popular program, but I suppose he also has a day job now.