As <PERSON> said, you won't know for sure until you do a finite element analysis. I was intrigued by this question as a colleague and I got into a discussion about this. While we both agreed the diagonal bracing would be better at resisting deflection, we wondered by what factor it would be better.
We were really curious so we settled the debate and did a quick structural analysis on SkyCiv Structural 3D (can try for free for one month if anyone is wondering). It took around an hour to set up both gates and analyze them mainly because we had to generate the node positions from scratch. Anyways here are the results of the linear static analysis which take into account the assumptions and simplifications you made. We applied a 5 kN POINT LOAD at both F1 and F2 and made each support a pin support at the locations you specified. 441
Note that in the 3D colored results the deflection is 12X greater than the actual deflection of the gate in both scenarios - it is exaggerated so you can see the deflected shape of the gates.
Gate #1
$\text{y-deflection at the bottom-left of the gate} = 31.74\text{ mm}$
$\text{Max total deflection} = 32.10\text{ mm}$
Gate #2
$\text{y-deflection at the bottom-left of the gate} = 7.84\text{ mm}$
$\text{Max total deflection} = 7.55\text{ mm}$
Diagonal bracing (Gate #2) is clearly the winner. So when both gates are subjected to the same load it looks like Gate #2 resists deflection better (i.e. is more stiff) by a factor of 4.25.
Some more interesting points:
* There's a pretty high bending stress at that top right support in both scenarios ~ 350 MPa.
* The analysis didn't take into account self-weight of the gates.
Also let me add that there looks to be a scaling issue with the diagonal grid you have drawn, because when I modeled it I found that there were far less points than what was suggested by your diagram. I ensured that the parallel spacing between each rhombus was 300mm. This means the diagonal of each rhombus is roughly 424mm. Your gate is 3300mm in length so that means around 8 rhombi should fit across your gate in the x-direction - but you've drawn around 12. Just thought I'd let you know. 441