There's more than one kind of "one year visa", and they are awarded on the basis of marriage to a Thai national, retirement age 50+, job offer with licensed company, enrollment in an accredited institution (study), and in some cases "volunteering" with a valid organisation who can prove they need you. I got mine in Vientiane and it was just as easy as getting a tourist visa, but of course I had all the required supporting documents. Also note that initially you get a 90-day entry then you can extend a year. See the link for what is required:
I'd definitely go Savannakhet over Vientiane unless you want to hang around the Lao capital... The folks in Vientiane "misplaced" some documents sent from the Bangkok foreign ministry supporting the Non-imm 1-year visa I got last January... It finally turned up, but only after I'd been forced to spend Christmas and New Years alone in Vientiane. Regardless Vientiane usually has a much longer queue. Savannakhet usually has no more than a 15-minute wait - been there twice and both times were easier than any of the other embassies (or consulates) I've hit so far.