Using 3" (or 4") recessed lights with GU10 bulbs for ambient (not accent) lighting
The light fixture you are showing are for retrofit installed through a hole. If the basement is unfinished you can just use 4" can lights for new construction. Then you don't have to throw away the halogens and can choose the color of your LED light kits from 3000K to 5000K whatever pleases you.

As far as the spacing, the picture you show looks like way overkill to me. You could use half that many lights for ambient lighting in a basement, especially with the newer 12 watt LED's at 650 lumens. A Google of halogens shows 50 watt lamps produce 430 lumens at 2750K so they are yellower and dimmer and use much more electricity.

The spacing doesn't look right by the rule of thumb. It looks symmetrical but the rule is to space the fixtures in the middle of the room double the distance the first fixture is from the wall. More to the point, if the first fixture is 2 feet from the wall the next fixture is 4 feet away from the first. Since there is no light at the wall the first one needs to be closer to the wall. From there you are always between two lights so they can be further apart since they light the room from both directions.

Good luck with your project!