OS X doesn’t support the TRIM command (which is usually tied with the OS and an NTFS volume), however, a few benchmarking have apparently reach the conclusion that OSX’s performance with an SSD drive is not affected like it was in Windows (with TRIM Disabled).
In other words, Windows without TRIM suffered massive performance degradation over time. With TRIM, Windows did well.
OS X, on the other hand, having no TRIM support, didn’t suffer the performance degradation in the first place. The interesting article can be found here at bit-tech.net.
TLDR Version (and I quote):
While we know SSD performance is affected by the OS - after all, you need Windows 7 for TRIM support - but for OS X not to suffer from performance degradation when it's using an SSD seeming stunning to the point of being difficult to believe.
TRIM aside, your battery problem might be mitigated by a few things and there are a few recommendations about how to make it work better under OSX.
The original article is a blog post found here which I suggest you read for more detailed information.
Modify Sleeping mode so it doesn’t save the content of RAM to drive when closing the lid (if you do this and remove the battery while in sleep, you lose the ram contents and will have to restart your computer).
Hard Drive Sleep: turn it off, SSD has no reason to go to sleep.
Sudden Motion Sensor: You can also disable this, an SSD has no moving mechanical parts that may be affected in case of a sudden impact.
Enable noatime for SSD filesystems. This will make the SSD write less info. (If you’re using FileVault make sure you read the article)
Spotlight: The article suggests disabling it if you don’t use it, but I wouldn’t do that.
On top of all that, I recommend you do a few things:
Check this question and answers on this site about how to identify possible CPU processes that may be hogging your CPU and therefore eating your battery life.
Perform a full battery cycle charge. All the relevant information is in Apple’s Battery Page, which is linked in this question on this site too, with some more interesting links you might want to follow.
To address your question, it shouldn’t happen, as SSDs are usually more energy efficient than mechanical drives. I bet either spotlight or time machine are doing some work and draining your battery life.
Try starting your machine in safe mode (hint: press ⇧ shift after the chime) and monitor your battery life there. Don’t forget to perform the battery tips before doing that.