From what you've mentioned you like, I think you might really like both GURPS and HERO (using Fantasy HERO). Both systems are modular, and you can "dial" down (or up) the grittiness, realism, lethality, and magic.
GURPS has a standard magic system which is very different from D&D. I love it, and will always love it, but it is very different. They have a newer book out (GURPS Thaumatology) which gives you tons of rules ideas for different systems of magic. If you want MORE of a D&D flavor with GURPS, check out GURPS Dungeon Fantasy, which is a series of inexpensive PDFs which expand the GURPS rules to simulate 'old school' D&D. GURPS Martial Arts provides a TON of cool options for realistic martial combat (like reversed grips, defensive grips, training in techniques). Do note, however, that GURPS provides very little support akin to "adventures" or Monster Manuals.
HERO is a very flexible points based system. It is a little more 'cinematic' than GURPS, at a default, and does not handle skills, advantages, disadvantages, and combat in nearly the incredible detail that GURPS does. However, it is much easier to be "cool" in HERO without costing 800 points, like in GURPS. Fantasy HERO is their basic supplement for running fantasy games. Note that this is a toolkit, and not a setting. It gives you quite a few different fantasy setting ideas, but does not flesh out any of them. There are Fantasy HERO Grimoires (full of magic spells), Fantasy HERO Bestiary (a Monster Manual) and other supplements full of pregenerated characters.
Both GURPS and HERO are toolkit systems. They do not seek to create any particular "feel" in their games. That is left up to the DM. This means that you are both considerably liberated, and considerably burdened. The game can be (almost) whatever you want it to be, but you also have to do a lot more of the work. Co-running a fantasy campaign in GURPS took up quite a bit of my time, and due to the detail of the system, we typically had about 2 RP 'encounters' and one or two combat 'encounters' in a six hour session. Combat can take a long time, particularly in GURPS, though it is also possible to outmatch (or be outmatched) in a fight and have it end very, very fast.
One of my favorite parts of the system for GURPS: character points. Heroic Characters are usually built on 150-250 points (plus probably another 50-100 in disadvantages). This means that you can give meaningful 1cp awards to players without screwing up the game. I gave out 1 cp per session just for bringing snacks!
GURPS lite is a great suggestion. It's free, so you can try it out at no cost, and, if you like the game, it is really all that your players will need to consult.
