What is there to like about the AMD Radeon HD 6450? Well, not too much. It is good enough for desktop use with a composited window manager and for video playback (assuming you're using Catalyst to take advantage of the UVD3 engine via XvBA). The PowerColor Go Green! AX6450 is a low-profile passively cooled graphics card, which makes it a potential nice fit for SFF / HTPCs.
Beyond those areas, there is not much to enjoy about the Radeon HD 6450 if you care at all about OpenGL performance under Linux. Even with the performance-oriented Catalyst driver, the performance of the Radeon HD 6450 with DDR3 video memory is crippling slow, as these benchmarks show. The GeForce GT 220, GeForce GT 240, and even the GeForce 9500GT and GeForce GT 520 were faster in a number of the tests. The HD 6450 though is at least a definitive improvement over the previous-generation Radeon HD 5450.
The PowerColor Radeon HD 5450 is currently selling for around $50 USD retail where as the NVIDIA GeForce GT 220 meets that same price point and there are even GeForce GT 240 graphics cards for $55~60 USD. Knowing that, the NVIDIA GeForce GT 240 (or even the GeForce GT 220) is a tremendously better option than the Radeon HD 6450. The performance is much better and the proprietary NVIDIA driver video implementation with VDPAU is superior to XvBA with AMD UVD3, which makes it a better candidate for media / home theater PCs.
About the only reason you'd want to stick with the Radeon HD 6450 over NVIDIA's low-end graphics cards is if wanting to support AMD and their official open-source strategy where as the open-source NVIDIA Linux driver is developed entirely by the community without any form of support from NVIDIA Corp. At this time, the open-source Radeon Linux driver is superior in terms of the feature-completeness (e.g. power management) of its DRM and Gallium3D components compared to Nouveau.
Hopefully the AMD Radeon HD 7450 will be a more compelling product...