in terms of performance, this would beat out a dual core Atom, but not by a huge margin. Roughly 20%, by any benchmarks I've seen. And you're easily looking at 5x the power consumption. Yeah, noise won't matter much if it's in the basement, but power consumption will, especially if you will be running it 24/7 (the P4 has much less power-saving options. I am not sure if it can downclock to save power when idle like new machines can). Remember, this is one of the old PGA479 P4 Xeons, not one of the newer LGA771 P4 Xeons. There are some 1U dual core Atom barebones around the $300 range, but that $200 price difference will be realized within your first year of ownership, on your electricity bill.
It has only SCSI/IDE support, there's no SATA, so forget about swapping out those hard drives with something newer. There's no eSATA or USB 3.0, so forget about a reasonably quick external hard drive. There's 8MB integrated graphics memory, and only goes up to 1600x1200 (most likely, this is VGA-only with no DVI or HDMI), so forget about doing any HTPC type tasks on it, you'll be limited to using it as a fileserver. There's no PCI Express, so you can't even go add a SATA or USB 3.0 or discrete GPU card. It uses ancient DDR, which is becoming increasingly hard to find. No $30 4GB memory upgrades here, you're looking at 1GB sticks that cost like $40 each used, because of how hard they are to find.
For a HTPC, you'd get a lot more mileage of anything Core 2, Athlon 64, or newer. They will run cooler, and have SATA, and have PCIe so you can use a modern low-power GPU with HDMI. For a file server, you'd do a lot better with an Atom mini-ITX and a PCIe RAID card, because they don't need that extra ~20% performance that the dual P4 has, and the tiny power consumption will really help electricity bills for a machine that's always on.