Cheaper and way more versatile. Anything you can do on the TRX you can do on rings, and way more.
Only potential benefit of the TRX is that it might be more gentle on the hands due to the rubber handles. But after a few weeks of gripping and exercising on the rings, you'll be fine.
Yup, definitely go for wooden rings if you can. They are much nicer to use than plastic rings or the TRX handles. Plastic rings get all sweaty and slippery and the handles only really have one holding position.
Pullup and dip have a new style of hybrid rings in their new kickstarter which I am interested to try. They have both a rounded ring side and a flatter handle side. You can see them on the campaign images - doesn't look like they sell them separately yet.
https://www.kickstarter.com/projects/pullupanddip/freesixd-w...
Cheaper and way more versatile. Anything you can do on the TRX you can do on rings, and way more.
Only potential benefit of the TRX is that it might be more gentle on the hands due to the rubber handles. But after a few weeks of gripping and exercising on the rings, you'll be fine.