Hi Bothfly,
I've used a 6020 for thousands of hours, in both jet and turboprop aircraft, and I love it! However, the service problems noted will affect you most certainly.
The nice thing about the Sony is that it has no rabit ears or exposed wiring like the telex, sound quality is excellent and it is VERY comfortable to use. It would serve you on the 737 very well.
The problem is service and parts. Since you fly for SWA, I would assume the headseat would see heavy usage every day, with lots of on/off cycles. The cord will become frayed, and when mine did, I had to send it in to be replaced, which isn't an option anymore with all the service centers gone.
The other issue is the lack of any replacement ear pads. The pads on the Sony 6020 will last you about 2 years of heavy use. They are odd shaped, and replacement pads for other headsets will not work. I when I started using the headset again after a hiatus, I called around for replacement pads, and wound up getting a few from Sony, and a few more from Hart Aviation. I have about 10 sets now, enough for the expected lifetime of the headseat, and then some.
If want to get the 6020, make sure you get at least a few extra sets of ear pads from someplace before you buy. Once you have it, I would wrap the cord with one of those spiral plastic cord protector things you can get from Radio Shack. With that, you should get 4-5 years out of it, and then you could probably get some sort of avionics shop to replace the cord if you need to.
Best,
Nu