Neither dress looks like a maxi to me, either. As Tam noted, maxis would be longer.
The first dress looks dated because the length really is not long enough to look like a maxi. Plus maxis are more flowing and unstructured in my mind. This looks like a long sheath. The print also dates it a little for me. It's not quite ditsy floral enough to make it look like the floral patterns that are on trend.
The second look is much better to my eye despite the fact that the length is not ideal. The accessories make all the difference. The shoes and cuff lend edge.