My first thought would be slider, but I guess it might come down to the "extra cost"

Slider is a standard option no cost. extra cost is for the in swing door.

The pro of an inswing door would be if BOTH sides of the door opened so that you have at least one door in the home where you can bring in oversize items or if someone is injured/sick you can get them in and out of the house if needed. If your photo is correct, the option he is giving you allows only one of the doors to open. If you are going for a more modern look, the doors without the grids would be less traditional.

Yes! the option of swing door allows only one door to open. Which door is more secure and safe?

No significant safety difference. Doors only keep out honest people. Most doors are kicked in and it takes only a couple of seconds. You could put all kind of locks on either of them, but all one has to do is pick up an object and break the glass in a door or window if they wish. Get the one you like the best and put in a good security system (and that is not fool proof either).

They are full glass. If someone wants to break in, they can always break the glass. The double door with inswing and center hinge is usually not terribly secure as it can be kicked in but you can use a deadbolt to help with security.

Sliders can sometimes be taken off the track. We have a drop-down bar (easy to buy and install) that goes across the center of a slider to prevent the door being opened/taken off the track. So the glass would have to be broken to get in, as near as I can tell. It was already on the door when we moved in-- I would probably not have installed it.

If both doors on the inswing were operable, that would be my preference because I could open up a wide area for passage back and forth to the deck and have nice breezes (hopefully) coming through. But since one door is fixed, I would get the slider because it won't take any swing-space into the room.

If you don't want someone to break in as easily, use a solid door with a deadbolt into the wall side.

Just my opinion :)

I never like in or out swing doors they take up space and provide no real advantage unless both open wide to allow large items .

I would choose the in-swing doors. They have higher energy efficiency than the sliding doors. A seal between the two sliders is not so good and a door that closes against a jamb is more air-tight than a slider. Also, the flush mount in-swing looks better and the grills obstruct the view.

-- amateur but recent window and door purchaser

Benefit of insulation is relative to your climate. We prefer a sliding door because we don't have a lot of room to open door onto our deck and not hit the outdoor table. You should be able to remove the grid if you want a more modern sliding door.