Mechanically, they are best for classes which can't get a lot of AC easily. For example, a tortle druid starts with 19 AC. Finding non metal armor that is going to get you to that level is VERY difficult. (Dragonscale can do it IF you have 14+ Dex, and uses an attunement). Also since you have proficiency in Claw attacks, your wildshape forms with claw attacks would get to use your characters proficiency when it is higher.
A wizard/sorc/warlock might appreciate it as well as it lets them focus less on Dex. (Mage armor needs +4 dex mod to hit 17 AC)
Tortle would also be a very good Str rogue, as 17 AC is the same as Studded + 5 dex mod. AND as it isn't heavy armor, has no penalty to stealth.
Barbarians are also decent choice with tortle, normally starting with for example a +2 Dex and +3 Con mod starts them at 15 ac. EVENTUALLY they may get half plate or +5 Con, but thats down the road with its own drawbacks (such as stealth disadvantage, or delaying str or other feats) Where the Tortle will start with it.
Basically the Tortle in general should start off harder to hit, but might eventually be better off with armor. Most notably, if you have the defensive fighting style or find magic armor or plate armor early.