A friend of mine bought one of the high dollar BOSE iPod systems which I found very impressive, and which my wife became enamored with. I, however, was not inclined to spend $500+ on a boombox, refined or not.
The Kicker iK501 is actually a bit bigger than the BOSE, and sounds quite good. On the down side, it doesn't sound quite as refined as the BOSE, and if you want to use it outside, you don't have the rechargeable battery thing that the BOSE includes. The iKicker only works plugged in to the wall using its' "brick" in-line power supply. You don't get battery operation - or battery woes - with the iKicker. Both Bose and the Kicker sound very clear and have the "good-car-stereo-sound-in-a-box" thing down pat.
The iKicker has deeper and louder bass than the Bose. I haven't measured it, but my ear is pretty good from listening to high end stereos over the years, and I suspect that the Bose system is probably better EQed for smooth, flat frequency response and there is clearly some level dependent EQ going on that I suspect is tweaked to match the human ear at various volume levels. After all, that's how Bose made their bread-and-butter with the 901s 40 years ago: Dr. Bose's little speakers sounded fantastic with the equalizer before the power amp in the circuit turned on, and lame as all get out without the electronic equalization.
The Bose has no tone controls at all: the iKicker has Treble and Bass that you can adjust to taste and volume level to get a ***VERY*** good sound, which is fairly comparable to the Bose. Listening to acoustic music through either system is great. The iKicker sounds clear and not overly colored by the speakers, although I do think the Bose is a tad more "neutral" sounding, which may or may not be good depending on your taste. For Rock and Roll, I think the sound of the iKicker is actually a bit better than the Bose, and although I'm not into it, I'm sure the hip-hop crowd would think the Bose is lame by comparison for that genre. The iKicker has a passive radiator on the back driven by the woofers to augment the bass, and you can hear and feel it working. The midrange is clear and well-defined. Crisp highs make the high hat sound like it's in the room. And did I mention the iKicker can get LOUDER than the Bose? It can probably keep up with most house party crowds; I doubt the Bose could cut it.
I use a 4th generation iPod Nano with it, and the remote control works the Nano as best I can tell, although I haven't really spent the time to figure out the iPod OS in great detail. But it does all the basics if you are too lazy to get up off the couch. It has a blue display to help you make adjustments to volume, tone, balance... the usual suspects.
But the *really* big plus over the Bose is the PRICE, WAY less than half of the cheaper Bose, and less than a third of the good one. I think I got it for around $165, IIRC, which I thought was within reason for a **very** nice boombox that can keep up with the "big stereo" in most of my friends' living rooms. Of course you have to add the cost of the iPod to that, but you end up with a great-sounding jukebox you can move around without much hassle that will play *all* your music without the hassle of changing CDs, and with NO fragile, dangley cord attachments. The only dangley part of the iKicker is the power supply brick, which is pretty substantial and looks sturdy. No puny connectors or chords. The iPod plugs right in in the front just like the Bose system. Construction looks solid.
I don't think anyone could be all that unhappy with either system. But for my money - and I LIKE good sound systems - the iKicker makes more sense.