I assume you are talking about the Ti 4400 and didn't just add an extra zero on the end of the Geforce MX 440.
In older DX 8.1 based games, the Ti 4400 will have the 5500 for lunch because it has more memory bandwidth, a higher fill rate and it can push many more verticies per second.
The FX 5500 has hardware support for a lot of pretty new shaders, but doesn't have the memory bandwidth or enough rendering pipelines to be able to play games that use those new shaders (like Doom 3) at a decent resoultion. In fact, the FX series doesn't quite pull of DX9 correctly enough for Half Life 2, and the game falls back on DX8.1 rendering paths when it detects a FX-series card. The upshot of this is that in HL2 the graphics not only don't look any better on the 5500 (despite it being a DX9-level card) but the Ti 4400 will be markedly faster.
Another option might be to sit tight and wait for the 6600GT AGP card to hit the store shelves in good quanities in a few months. They ought to finally push down the Radeon 9800 XT and Pro prices, which will hopefully have a dominio effect and get the 9600XTs down around the price the FX 5500 is now.