The only problem with the Sony MZ-RH1 and ECM-719 combination is the Sony ECM-719. Don't ever use a Sony mic. The MZ-RH1 or the iHP-120/140 will make great recording when combined with an inexpensive battery box (I use Chris Church's tiny one-about $52 on E-Bay) and Sound Professionals or Church Audio omnis or cardiods costing around $120 or less. Do not use a mic that attaches directly to the recorder-get a corded one. This avoids any chance of recording noise made by the recorder. If what you are recording is fairly quiet, you may need a pre-amp instead of a battery box (or you can try battery box into mic in instead of into line in), but this is rarely a problem with rock concerts. It is very stealthy, and if you need to record longer than 94 minutes without changing discs, to my ears Hi-SP is basically indistinguishable from PCM. With Hi-SP you can record over 7 hours on 1 disc. The battery will last over 7 hours in that mode also.
I have made great recordings with my MZ-RH1. I don't care for having to use Sony's software to upload, but it's not that hard to get used to. The only thing I really dislike a lot about the MZ-RH1 is that when using line in (which is generally best when you have a battery box), the recorder automatically starts a new track when the volume drops enough. They can easily be combined and tracks put where you want them with audio editing software, however.
I also recently picked up the iHp-120 and installed Rockbox. That shows great promise as well, but I haven't yet made a recording with it combined with a battery box (or pre-amp), so I can't report on it personally. From what I see on the internet, it will make great recordings with a pre-amp (the Church Audio ST-9100, which I have ordered, is highly recommended) and probably, in many cases, with just a battery box. I like the fact that you can upload the iHp-120 recordings by drag & drop and that it doesn't arbitrarily start new files when the volume drops. (I made one recording using just the recorder's internal pre-amp. The loud parts sounded great, but the quiet parts were fairly noisy.)