I enjoy sports games that play more like wargames. Time and decision making invested in moving players around a field and performing the actions associated with the game (be that NFL or soccer or whatever else).
What I dislike:
I don't enjoy games where I spend my time staring at charts or spreadsheets, comparing stats and concluding that it was a gain of three yards. Calling the play is fun, but I feel disconnected to the play when I'm not taking an active part in how it unfolds.
Favourites that I've tried so far:
Technobowl with the fanmade rules variant is a wonderful arcade implementation of football and I used to be a Bloodbowl player (but that feels a little too far removed from the actual sport). What should I try next? It would be nice to have something that does this element well, whilst also playing out with a little more accuracy in simulation.
Sounds like you need to look into PC football games. Action PC Football fits fairly well into your criteria.
Other folks might have suggestions that are better. Action is the only PC game I own. I prefer the C&D games.