I have used both and the drip system is much better in terms of saving water. I don't think the gravel would be a problem if you are mowing grass, as you would have your blade high anyway to further save water.

Have to agree with VBain. Set the mower as high as it will go and the gravel should not be a problem. Your plants (grass?) will thank you for not scalping them within an inch of their life. Bear in mind that there is a direct correlation between the height of the grass and the depth of their roots. You want those roots deep in the soil.
The drip system is superior at getting water to the roots of the plants without all that loss to evaporation especially in your (dry) climate. I find it impossible to get water that deep into the rootzone effectively and without waste using a sprinkler.

Thank you both so much! I feel very reassured to move ahead now with gravel and a drip system. Oddly enough I read someone else's question about burning or mowing their meadow and while trying to answer something occurred to me. I could just use a string-line mower to keep away from the gravel. Duh! Lol!! Thanks again- I'm really looking forward to the projects ahead and how different this place will start looking!- Lou