My wife and I have done both, in both directions (different years). Not surprisingly, there's advantages and disadvantages to both.
We actually rode the L&C before ACA mapped it; we followed Hwy 12 along the Clearwater River through Orofino, instead of climbing up and over the high plateaus near Clarkston. There was traffic, sure, but the highway was OK.
The major difference is that the TransAm (from Kooskia to Astoria) is longer than the L&C. For us, the TransAm took a week longer. So if you're time-constrained, riding down the Columbia might look attractive. Quite a few people finish up the TransAm by taking this route and cut off the extra miles.
Jamawami has good alternatives, and he makes a good point about the wind. In summer the winds howl out of the west up the Gorge. There's about a 50-mile stretch where a westbound rider can expect 20-30mph headwinds. You could say that the scenery makes up for it, though. And for 150 miles along the Columbia you have only a few (relatively) minor climbs.
On the other hand, the TransAm goes through Hells Canyon and the high desert of Eastern Oregon. Depending on the year, you can expect 100+F temperatures. You'll have wind, too, but not as predictable as the Gorge. Plus lots of 4000+ climbs.
So you take your choice. Either is classic western cycling country, and the memories of headwinds or heat will fade once you make it to the coast.
One route we took combined both: Ride the TransAm into Oregon. Climbing out of Hells Canyon, eight miles west of Oxbow turn onto North Pine Rd (FS Rd 39). This takes you along the Imnaha River and eventually to Joseph. The ride through the Wallowa Valley is one of the most magical tours you can imagine. To Elgin, over the Blue Mountains and into Umatilla, where you join the L&C. It's pretty remote in the Imnaha region, but good FS campgrounds. Camp at Wallowa Lake State Park and you won't want to leave.... See here for the route
. This is the best part of Oregon for touring, IMO.
Good luck, great ride.