Both are great bikes. I'm assuming the CRF that oats is referring to as not being as trail-oriented is the CRF150R, which is true. It is more of a high-performance, 4 stroke replacement to the old CR85's. However, the CRF150F and the TTR125 are essentially the same bike, just a different manufacturer. I have ridden, raced and sold both Yamaha and Honda, and you really can't go wrong with either.
Honda's tend to be a little more expensive, but if you're going used then that shouldn't be an issue. I always felt the Yamaha had a little stronger motor, even in their race bikes, but the fit and finish as well as engineering of a Honda can't be beat.
The one thing that will most likely make the difference (although I'm not 100% on this), is going to be electric start vs. kick start. I believe the Yamahas have had electric start on the 125's for a while now, but I think Honda may have just started doing it on the 150's just recently. If you find used ones more than a couple years old, this may be what helps you decide.