I'd have to go with the original system; lose all rings, can recollect up to a relatively small amount. Here's my reasoning: Let's face it, Sonic has it easy (as far as health goes) compared to several other platformer-oriented characters. Let's use Mario as an example.
In the 2D games, Mario starts as his short, basic form. That is considered his vulnerable, "one hit to die" form. Among the multitude of items he can grab, most of the power-ups will transform him in some way, giving him additional chances. Based on the western SMB3, you first need to collect a Super Mushroom in order to then upgrade to the Fire Flower; the game rewards you for surviving without getting hit long enough to get a more powerful upgrade, which you will lose if you get hit, but you'll still be the big (Super) form. The better you perform, the stronger you become.
In the 3D games, Mario has health points, which are self-explanatory. The number of health points varies, but should he lose them all, he loses a life. The max health to danger ratio is usually well balanced; for instance, you have more life in Super Mario 64 than you do in Super Mario Galaxy, but there's also typically more chances to get hurt. Mario can regain his health points by different means, such as coins, but they are somewhat scarce.
Now, let's take a look at Sonic. Typically, his levels are a little more dangerous than Mario's; Badniks vary a lot, but the amount of traps set around stages is usually pretty high. Sonic typically has no way of gaining extra health, instead losing a life after any damage is received; he is always vulnerable, just like Mario's smaller form. To make up for that, collecting and carrying rings (in addition to bubble shields in most games) will afford him a chance to recover from an attack, reverting to his vulnerable self. However, unlike Mario's various means of recovering life or power-ups, rings are usually very abundant.
So why would I prefer the original ring system over the others? Because losing only some of your rings is pretty insignificant, merely a nuisance but no real danger due to the abundance of rings and the fact that you kept some of those that you already had; after all, it makes no difference whether you carry 1 or 999 rings, as far as health is concerned. Add the ability to recollect some (or all) of your lost rings to that, and you've got a pretty broken and overly easy system.
If instead you use the original system, then here's how I see things: You can gather as many rings as you want, and as per typical, you gain extra lives and a better score for getting and keeping as many as you can; it rewards you when you play well. Should you get hit, you lose it all, but the game at least makes up for it by allowing you to pick some of them back up which was very useful because you typically needed a certain amount of rings to enter Special or Bonus stages, and you can last longer against bosses, assuming you're willing to take some of your time to run to your scattered rings quickly while avoiding attacks. If you get stuck without rings at any point, the danger also exponentially increases from "Whatever, I have rings to cover my ass" to "OH FUCK I'm OUT OF RINGS", adding pressure onto the player. Those are some things I think have been missing in more recent games.
TL;DR: I think the classic system is both more rewarding, and depending on how you want to play, safer or more challenging.
EDIT: Corrected the amount of recoverable rings for accuracy; thanks to OL for pointing out my mistake. I'm pretty sure that 20 was the amount recoverable in SA1 and 2 though, but anything between 20 and 32 would be great.
This post has been edited by Kurosan: 20 August 2009 - 08:14 AM