I don't see how the built in battery is a problem. I've got 4x DualShock 3 and 2x original SIXAXIS controllers, and they're all perfectly fine and still last ages on battery. Really haven't run in to the issue of a dead controller, and my pair of PS3s get a lot of use.
My 360 on the other hand? I've got 4 controllers, and am down to one working original battery. I went out shopping for new batteries, and to my shock the only way to get official Microsoft batteries these days is to buy the Play & Charge kit. Hold on, I've already got two P&C cables, I don't want more! Luckily I found a Blockbuster that had a single battery sitting on the shelf from old stock, so I'm now up to two.
In my experience the 360 batteries have been unreliable (3 died), and then to top it off are now not available on their own. That removes any kind of advantage they had over the PS3's built in ones.
Oh, and I've had a dead Wii Remote too. What's worse that was the entire thing, not just the batteries.