The choice is purely your own; if you want to browse text-only, you have a lot of options available to you. links and lynx are just two of them.
Each has its own style and presentation; lynx appears to handle colors well, but links is not trapped in black-and-white, either.
Each one is speedy and faithful to text displays, and if that’s what you need from a text-based browser, your life might be complete on that note.
Web jockeys in the post-2.0 era will insist that very little gets done without AJAX or Flash 10.X or embedded 1080p video playback, but at the risk of mincing words, I think that’s a load of crap.
Use whatever gets the job done for you. I can breeze through my GMail accounts in a third of the time with either links or lynx, as it takes with Firefox 26.0011, a/k/a Firefox The Pudge.
Point being, don’t let any screwball Internet pundit tell you text-based browsing is passé. Being a screwball Internet pundit is passé, if anything is. 😈