Stu – the FT-450 is a very powerful radio with the IF DSP. I have a friend that has one and have enjoyed using it. I wouldn't mind having one myself. To your point of it costing less – it does. However, when you consider the portability of the 897 and 857 plus the 2m/70cm I think the price difference is WELL worth it.
Keep this in mind too – the current draw of the FT-857D/897D is ~500mA. I measured my FT-857D at 650mA, but it may change between specific units. You will NOT get close to that current draw on RX with any IF DSP rig. Both my other HF radios draw a solid 2 amps – TS-2000 and IC-718 (though the IC-718 has AF DSP and no filtering, not IF DSP like the TS-2000).
I think the 2m/70cm all modes capability the FT-857D/897D is a major selling point. This is the reason I bought my 857D. If the FT-450 did 2m/70cm I would have been more tempted to buy one of those instead. However, the FT-450 still won't satisfy the mobile and portable need that my FT-857D does.
My FT-857D goes with me on backpacking trips and is my every day radio in the truck. It has worked the world. I spend more time with the 857 than all my other radios combined.
For Bryan, the OP: In considering any of these radios, keep in mind that the IC-706mkIIg is 10+ year old technology. Maybe closer to 13 or 14 now. The FT-857/897 radios are around 6 years old. Big difference in technology. Also, Yaesu's AF DSP works better than Icom's because Yaesu put AF filtering in theirs. The noise reduction of both don't really help that much, though I wold give the edge to Icom there. However, the AF filtering does more to improve the useability of the radio than does noise reduction.
Depending on what your style of operating will be I would highly recommend the FT-897D, of the two. The reason is the ergonomics of the radio. The bigger knob and layout of the buttons, not to mention the bigger display screen, make the 897D a much better radio to operate. However, if you need the remote face plate and compact size of the FT-857D (which I did) then that is still a great option.
I don't leave home without a radio, and the FT-857D is the only one I take anymore. Unless ham radio is the purpose of my trip (field day, operating from EN39, etc). Convenience can never be matched.
I am a CW operator and bought the 300Hz filter from Inrad (as well as a 2.0kHz filter for SSB). If you operate CW at all I would highly recommend this one. Don't bother with the 500Hz, its too wide. The 300Hz is fine – I can find stations all day long scrolling the band with it. I have only had a couple of occasions where stations called back to my CQ off frequency enough to not hear them. However, being so close to where I was I could detect a change in the noise of the band – that's how I knew they were there. Not a big deal for me.
Bryan – in any event, don't be scared of buying one of the yaesu radios! They are great. IF DSP is nice, but I have been using a TS-2000 for the past 6+ years as my main station radio and still went back to basics, so to speak, with the FT-857D. It has turned in to my main every day rig.
Though, if current consumption isn't a problem and you still want a compact radio that has IF DSP – look at the IC-7000. I have $1200 in my FT-857D (full set of filters, remote mic) and an IC-7000 is in the $1300 range. Looking at it that way the extra $100 is well worth the IF DSP, color display, and still having the full 160m-70cm band capabilities.