I own a Tascam DR-100 and in conjunction with a good shotgun microphone (although not the best on the market) the Tascam is extremely good quality and will give you professional recordings of the sound you want to capture.
I have used the R44 and it is a very, very good portable recorder, and I don't have anything negative to say about it besides one thing. It goes through batteries so quickly. I have tried so many different brands and when recording at only 96kHz (used as a reference frequency against other records not capable of the full 192kHz, such as the DR-100) I have only ever managed to stay in the field without a battery change for maximum 1 and a bit hours using one external mic with the phantom power provided by the R4. and just a little over 2 hours with the phantom power being provided via a battery.
The DR-100 however, has a Lithium Ion battery that I would trust to run my own life support machine. O.K. a little exaggerated but I'm sure you understand my enthusiasm. I was out recording on a film set from 10am until around 6pm this summer just gone and I had to change to the AA batteries at 16:30pm. this was quite a heavy recording sessions with starts and stops of recordings and turning the device on and off for set preparation for a minute or two. This is whilst it is providing the phantom power for a RODE NTG2 shotgun.
So the Lithium Ion alone lasted 6 hours (of course this number will change due to not recording constantly for 6 hours) However you can see that having that powerful internal battery is a definite advantage for sound designers who are out most of the day collecting material.
As for the AA batteries I have only ever used 2500mAh rechargeable and whilst providing the phantom power, I would say you can get 2 hours out of them (it may be more, this is just an estimation).
So to summarize,
The Edirol R44 has fantastic quality and 4 mic capabilities but will cost you an arm and a leg in batteries, not to mention the high price of the unit.
The Tascam DR-100 can record up to 96kHz 24bit but some sound designers will say this quality is plenty for most manipulation needs. (some may disagree) The built in Lithium Ion battery is a marathon runner and unless you get a defective one, it will carry you throughout the day. Finally you can buy a good mic and the DR-100 for the price of the R44, which, I'm sure most people with agree with me, is better than having a kick ass recorder and microphone with a rubbish frequency response. Quality mics are more important.
Neither units cause horribly noticeable amounts of operation noise or hiss.
My opinion, the Tascam is the choice for an independent sound designer like me. If you have the money to buy batteries by the barrel, go for the Edirol R44 to have that extra sound quality when manipulating your sounds.