The last two guys have you covered quite well. Being a Big Dog repair shop, I'll throw my

in. The 03's were still using a lot of Harley parts, but in 04 is when they started being a really refined bike. The 03 - 04's are still my favorite, because the are a lot smoother riding bike, as I'm sure the 05 chopper is too. 05 is when the government cracked down on emissions, so they went from the 107ci engine to the 117, and choked it down. The 117 is actually a detuned 124. So you will find the 117 has more vibration.
Over the years, a rumor got started about these bikes having electrical problems. This came about, mainly because people were buying cheap batteries. There was nothing wrong with the EHC's that came in them. The problem steemed for the fact that there wasn't any protection between the battery and the EHC. So if a battery shorted out or a voltage regulator shot craps, it would smoke the EHC.
When you get to looking for yours, remember this one important fact, most of us will testify to. Your Dog will find you. You will look at some and be tempted to buy out of eagerness, but we will tell you, you will know when the connection is made. My first one, was brought to me in baskets. Loved that bike.
Remember these bikes are 10 - 20 years old now, and most have been road hard and put up wet. But with the group of people that is on this forum, there isn't anything that we can't help you repair. And with HDM, Big Dog parts King, and Wild Steed worx, we have plenty of parts to keep these going for many many years.