I feel great in Atkins - I've honestly never met anyone who felt bad on it when following the diet properly (after the first week when the body is adjusting and many do feel bad), only people who eat too few carbs, too many or too little fat seem to.
Atkins involves eating high fat - so its not low calorie but you lose at a much higher calorie level. I wasn't losing at 1200 calories when calorie counting but lose at 1500 plus on low carb.
It's moderate protein so you can eat just about any meat with a focus on good quality whole foods and preferably avoiding processed things. Fish and dairy are great too.
It's low carb and you have to cut out all wheat - so no bread or pasta at all - and starches - no potato, oats, rice - and sugar - no honey, fruits except low carb ones (rhubarb initially and then certain berries). There are good replacements for most things though, like celeriac as a replacement for chips and cauliflower mash and rice. If you're doing it right you'll eat lots of the allowed veggies - I have whole veggie days sometimes.
Agree with Katie - it's a good idea to try any new thing for30 days to really test if it's right for you. I also followed low GI for a while but figuring it all out (some things are low GI when combined with others but not on their own etc) was overly complicated for me and I didn't lose much weight. I like Atkins for the clear cut rules.