Sit-ups are not an ab exercise; they target the hip flexors almost exclusively. Sure, the abdominals are involved in a postural stability role during sit-ups, but that's the case in almost every exercise imaginable.
Doing sit-ups as an ab exercise is like doing bicep curls for the front delts...pointless and ineffectual. There's another reason to avoid sit-ups (as well as leg raises, which are an identical movement, only with the upper body fixed and the legs moving): the hip flexors attach to and pull on the ligaments of the lower spine during activation. This means that sit-up and leg raise movements can exacerbate or even cause lower back problems.
There's no real reason for most people to train their hip flexors. They don't play any major strength role, and from a bodybuilding perspective, having defined flexors is more a question of bodyfat percentage than a training issue.
When it comes to ab training (and when I say abs, I'm referring to the visible, sixpack muscles of the abdomen) the crunch is king. There's a simple reason for that which ought to be familiar to anyone with a background in biomechanics: the rectus abdominis, which IS the "sixpack muscle", functions to curl the spine forward and reduce the distance between the sternum and navel. And this movement is the very definition of a crunch. Therefore, crunches and reverse crunches are the ONLY movements worth doing for aesthetic ab development. Core strength is a different issue, but even there, sit-ups do not play a role.
Your case is interesting for the following reason: When most people think they're training abs, they're actually hitting their hip flexors (as explained above). Since the flexors are far stronger than the abs, pure ab movements tend to be a hell of a lot harder to do than their faux HP counterparts. According to you, "sit-ups" are easier for you in a legs-flexed position than when your feet are on the ground. Now, when the legs are fully flexed at the hip, the capability of the HPs to engage in trunk flexion is significantly reduced. Therefore, the abdominal muscles account for most of the movement. Your abs would seem to be stronger than your flexors -- very strange, indeed. There is one relatively simple explanation, however.
Newton's 3rd law states that for every action there is an equal and opposite reaction. This can be applied to hip flexor training. Ordinarily, sit-ups are done with the feet held down in a stationary position, either by a person or by a pad. When the movement is executed, the tendancy of the feet to rise is counteracted by the resistance of the pad (or the spotter). This resistance is the "opposite force" which the feet ordinarily push against in order to execute the movement. When there is no resistance present, either one of two things will happen:
1) having nothing to push against, the feet will rise in an attempt to execute a classic, hip flexor-only situp.
2) if the feet stay on the floor, the abs will largely take over for the HPs and the movement will be converted to a crunch.
I say "largely" rather than "entirely" in #2 because it's still possible for the HPs to play an active in an unrestrained sit-up. There is, after all, traction between the feet of the participant and the floor, by means of which he can "push against" the latter and activate his HPs to execute the movement.
Here's the bottom line: Always do conventional crunches and their reverse counterparts with HPs in 90 degree flexion. Forget sit-ups. Learn how to do reverse crunches - if you can do an entire rep on your first attempt (or second, or tenth!) you aren't doing them right. Reverse crunches are probably the hardest exercise there is. Remember, ab training consists of flexing the spine. You can either initiate the movement with your torso, as in a conventional crunch, or with your pelvis, as in a reverse crunch. But if there is a change in the angle at the hip, you're no longer training your abs. What's the secret for real ab training for fat-or-weak bastards who can't do a single concentric rep? Slow, controlled negatives. And there you have it.