Peter - generally I'd agree with Jules' recommendation - especially if you're trying to photograph the smaller birds, a 400mm, especially if you have a 1.4x TC to use if needed, would be the best overall lens to have. Just to warn you though, if you are using a crop body camera (APS-C) there will be times at Wakodahatchee especially where you may be too close to fit the birds in the frame. Some of the nesting birds, if they're still there when you come, are within 15 feet, and 500mm in 35mm-equivalent terms is too much lens to fit them in the frame. Sometimes having a slightly shorter focal might be good - maybe even keep it in the car if you can, or bring one along...that 70-300 could come in handy in a pinch for those situations. If you're shooting full frame sensor, a 400mm plus a TC would be a pretty solid choice - 80-85% of your shots could be covered with the TC, and another 10% or so without the TC - there would only be a few situations where a bird may be a little too close to get.
I typically walk around both parks with a 300mm prime and 1.4x TC, on an APS-C crop body - so I'm using a 630mm-equivalent focal crop - it works for probably 80-90% of my needs, only occasionally being a little too much lens for the situation - if I pull off the 1.4X TC, I can pull it back to 450mm equivalent which helps. At Wakodahatchee though, I've gone birding with a 200mm equivalent lens and still been able to fill the frame without cropping, for some of the closer birds.
