How do people feel about the 135L with an extender?
It takes the extender ok, but it will lose to the 70-200L f/2.8 IS II in IQ/IS. If you don't have 70-200L zoom, then 135 + extender is a good way to extend the focal length range.
Do you think it is better than the 70-300?
The 70-300L will have better IQ than the 135L + 2x. The 70-300L matches well against the 70-200L f/2.8 IS II. The 70-200L f/2.8 IS II focuses better on lower contrast targets, tracks better, and has a 1-2 stop advantage but is heavier than the 70-300L. The 70-300L is compact and lighter, costs less than the 70-200 f/2.8 IS II, and delivers IQ that nearly matches the 70-200L over much of the overlapping range and is better at 300 than the 70-200 is at 280.
For those that shoot sports and portraits, the 70-200 f/2.8 II is the ultimate zoom lens but is heavy. It also takes extenders well. The 70-200 + 1.4x will nearly match the 70-300L at the long end and will be a stop faster, and the 70-200 + 2.0x will come close to 100-400L. The 70-300L is arguably the best travel lens. For controlled portraits or when trying to maximize discretion (although a dSLR with a L lens will likely be much larger than what many people use, i.e. cellphones) or going for the shallowest DOF/maximum background blur, the 135L is a good choice, but for most other use cases, the zooms are better.