This is going to be really brief as I need to get my son to sleep -- but the bottom line is: It depends.
The Bat! is without question the most powerful mail client you'll get your hands on. It is not, however, without its weaknesses -- there's a steep learning curve if you really want to take advantage of it and its search, while powerful, is nowhere near the speed of M2. It really depends on what you need. With huge mail bases, M2 runs into some issues -- namely the entire Opera application slows to a crawl when sending/receiving mail if the panel is open -- while TB handles large bases effortlessly. What I like about M2 is that it's like gmail, in that it's one big flat database that you can quickly search and/or apply labels.
TB is more organized -- For power users who want to take complete control of their mail, TB! is -the- way to go -- but for simply casually checking your mail throughout the day, I'd go with M2 -- it's free, lightweight, fast and the search makes of for the awkward folder structure. The Bat, on the other hand, is ideal for organizational freaks who like everything in a folder based hierarchy -- with its powerful filters, folders, virtual folders -- if you're willing to dedicate a lot of time, you can automate virtually everything but the actual converting letters into words, sentences and paragraphs
I also find Opera's keyboard editor more succinct -- and its documentation is unarguably more reliable.
But the bottom line--Opera is great for casual users, The Bat is ideal for those who want total control from the groundup.
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I think it's really cool the way they're embracing the open source movement and opening up to other operating systems -- it's a good move for them and endusers (and future endusers) alike.