You really do get used to the taste; after about a week it does start to taste somewhat normal. But I agree that in general, Diet Pepsi has it all over Diet Coke on taste. Diet Coke has always tasted like pure chemicals, whereas Diet Pepsi manages to attain some small shred of cola-like essence right from the first sip.
But then, there was a period back in the '80s when they were completely reformulating Diet Pepsi every six months or so trying to "get it right," while I don't think Diet Coke has ever been changed one bit from the day it launched, except for the switch from saccharin to aspartame.
(This is probably due to Coca-Cola's long-entrenched corporate cultural Prime Directive that sales of the flagship product was to be protected at all costs, and no product was to ever be produced that might cannibalize Classic Coke sales - and end up making Pepsi "number one" in sales by default. This is why Coke came up with TaB in the early 1960s, but never marketed it to anyone but extremely weight-conscious women who they knew would never buy a real can of Coke in a million years. It wasn't until Robert Goizueta was made chairman in 1980 that he finally was able to drag the company into the 20th century and get them to release Diet Coke at all. (A lot of people have always believed Diet Coke actually is TaB, but you can still buy TaB and they do taste different, IMHO.) And he was right; overall Coke sales kept going up, not down, and Coke remains #1 to this day. But I still think the company intentionally keeps Diet Coke tasting more like chemicals than Classic Coke in order to absolutely insure the flagship brand reigns supreme over their arch-enemy Pepsi.)
Along the same lines, I wonder why Pepsi One never really took off. It does taste more like regular Pepsi, though still not quite right.
For my money though, the diet soft drink that tastes most like the original is Diet Dr. Pepper.
Sadly, for the Atkins dieter, all of this is moot because you're not supposed to drink anything with caffiene, saccharin or aspartame in them, because it supposedly slows down weight loss in some people. You can get caffeine-free Diet Coke and Diet Pepsi, of course, but not aspartame/saccharin-free versions. You've only got one choice for that: Diet Rite cola. (There's a name I bet most people haven't heard for a long time!) They use Splenda® (sucralose) instead, which is Atkins-approved. Of course, most Atkins dieters just go for aspartame/saccharin soft drinks a lot anyway, especially since Diet Rite can be a bitch to track down in some areas, but technically, you're supposed to avoid aspartame and saccharin entirely.
Nutra Sweet (aspartame) is bad stuff. It's making people sick. See e.g. http://www.purehealthsystems.com/multiple-sclerosis.htm.