I think the first one you drew was E-hex-2-ene and the second one Z-hex-2-ene
Best, though, to avoid 90 degree bond angles.
However the one on the left has the terminal methyl group (the one on the end) anti-periplanar (180 degrees) relative to the double bond group where as the conformation on the right has the terminal-methyl group Syn-periplanar (0 degrees/directly facing) relative to the double-bond.
The following energy diagram below shows that actually Anti-periplanar conformations (two groups rotated 180 degrees relative to each other - *the lower conformation right in the middle of diagram*) are at lower energies than Syn-periplanar conformations (each group facing each other *the two conformations at the far left and right of the diagram*). This is due to steric repulsions between groups (like two magnets repelling each other at the + + poles.)
The diagram also shows the anticlinal and gauche conformations (which are at different angles - 120, 240 and 60, 300 degrees respectively).
This diagram essentially explains why the Organic Chemistry convention is to draw carbons in 'zig-zag' form and therefore why the one on the left would be more acceptable. It's a more energetically stable conformation and therefore more likely to arrange in that way.
Keep in mind though that molecules switch between conformations in the magnitude of e.g 20,000 rotations per picosecond. Very fast. Like everything in Organic Chemistry, molecules aren't in an absolute conformation. In reality, it's somewhere in between. However it's still a very good model for explaining a lot of Organic Chemistry in terms of energetics, stability of the molecule and why a reaction may or may not happen as a result of the geometry of the molecule.