There seems to be some confusion here.....
The softmod I'm refering to is a total softmod in the sense that everything is done with the software. You don't even have to open the xbox to do it, and once you get all your files ready, you can have it done in 10 minutes. If you go to the XBE exploits of the xbox-scene forums, you'll see what I'm talking about. It's very safe for beginners, it's cheap, and if something goes wrong, you can usually fix it as long as you have a backup of your eeprom. Softmods work on any version xbox.
Replacing the on board bios is better known as a TSOP flash. With a tsop flash, you have to open the xbox, jump certain solder points together, then reprogram the TSOP with a new bios. If you have a 1.0 or 1.1 Xbox, you can solder in switches that allow you to split the TSOP into 2 banks (2 x 512), or 4 banks (4 x 256). That way, if you flash one bank with the wrong bios, or if you like having multiple bioses (I switch between a two hacked bioses, a linux bios, and the original MS bios, which would allow me to play XBL if I wanted), you can do so. 1.2-1.5 Xboxes can be TSOP flashed, but you can't split the TSOP into multiple banks. Yes, if you mess up your TSOP flash, you'll need a modchip to fix it, but if you don't, then you've saved money that you would have spent on getting a modchip in the first place. Unless you mess with the TSOP flash a lot, you're probably not gonna have any problems with it once you pick a bios and stick with it. If your Xbox was produced anytime after March 19th 2004, then you have a 1.6 xbox which cannot be TSOP flashed.
Installing a modchip is the most secure method in terms of being able to recover from a problem, however, there are more things that can go wrong with it, and chipping an Xbox generally costs more than the other methods of xbox modding. Not to mention that if you mess up soldering, you could potentially mess up the modchip and/or your xbox. Modchips work on all versions of Xbox, however installation is different for certain versions, and if you have a 1.6, there are a few more steps involved, and you have to make sure you flash with a 1.6 compatible bios, otherwise you could brick your modchip, and potentially your xbox too.
Personally, I recommend the softmod, because like kaioshade said, you're just loading another bios, regardless of which method you use, and the softmod is the cheapest, easiest, and quickest way to get it done. I spent $10 on a used mem card, $7 on a used copy of Splinter Cell, and about $10 on a USB hub and a controller breakaway cord, which I used to connect my controller to the PC (with the mem card plugged in, loaded up the Action replay program (free on their website), and copied the gamesave exploit over)). For a grand total of $27, yes I could have bought a modchip (in fact, I did buy a DuoX2 for about $20 online, but that was for fixing an Xbox), but then again, I wouldn't be able to mod other people's Xboxes and charge them using that one modchip would I? :-D
After modding some people's Xboxes for about $20 each, I have more than made back the money I spent on the softmod materials.
And whoever said to use xiso to rip games, slap yourself. xISO is known for creating buggy ISO's, and it's been established for at least 2 years now that xISO should not be used for making ISO's. Qwix and Craxiton or much better Xbox ISO creation programs. For backing games up to the harddrive, DVD2Xbox is the best program to use, followed by Complex Tools.