Just play with it a bit. There's a ton of information you can get out of that which a parser or video won't or can't tell you.
For example, I looked at the log I linked and clicked on the Damage tab. If I hover over the players, it tells me their DPS splits. From that, I immediately know their Warrior's DPS is lower than it could be because his splits are off.
If you're a DPS, you can look at someones splits who is crushing you and potentially find a problem with your approach to a fight or even compare uptime%'s. You could be doing shit DPS simply because you're slow as fuck at getting from boss to boss.
It sounds like what you'll want to do is find the section of the fight you're failing and highlight (drag left to right on the graph area for healing or damage taken) and compare your HPS and your groups DTPS to another group. It'll also tell you how many things hit your team in this period and how many spells of each type were used.
It'll also tell you the contribution from your other healer in that period as well.
Edit: Basically, logs are god. There is no bullshit or excuse in the logs and that's why they're great.
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