Wiring from Main to Subpanel
Put a junction box inside the basement (i.e., right at the point where the wires exit to go outside). Romex on the inside (to make it easy to run it through the basement) and conduit on the outside (including through the wall and all the way down &amp; around to the subpanel) with THWN. One extra box and you get the best of everything. The box does need to be accessible - can be high up on a wall or behind "stuff" but not hidden inside a wall or ceiling.