Here's what we thought we were getting with ALR: Career, he's got a 109 wRC+ (including this season), so he's above average offensively. He's a career 1B, and has been 2 or 3 runs per season below league-average with the glove by the advanced fielding stats (although he's been above-average so far this season and was above-average last season). He's stacked up 11.3 WAR since 2004, and is generally good for about 2.5 WAR at 1B--a solid but unexceptional everyday player. After the jump, a quick look at how The Challenger compares!
Branyan has a career 112 wRC+ (also including this season and his time in both the AL and NL), also above average offensively. He's played the most at 3B, although nearly as much at 1B and somewhat less in the corner OF spots. At 1B he's about 5 runs per season above league-average by the advanced fielding stats, and he was above average last season and so far this season. He's put up 12.9 WAR since 1998, generally playing about 90 games per season.
On the face of it, it looks like Branyan and LaRoche are almost the same player--Branyan might even be slightly better. Of course, Russell has also struggled with the bat this year, putting up a 210/290/339 batting line for a 70 wRC+ (compared to ALR's 172/288/259 and 59 wRC+). They both hit lefty (although Branyan throws rightie). Branyan's platoon split is worse: his lefty/righty wRC+ is 82/121, while ALR's is only 90/115. They've both been good for 25-30 HR per 162 games, and 70-90 RBI (ALR has fewer HR but more RBI).
Branyan will be 36 this year, so he doesn't exactly fit the SPAD mold, and he has struggled enough to get released. Also, he's historically been better in the first half of the season, and he's been sub-par so far. Still, if ALR was a valid answer to the 1B question based on his career stats, Russell Branyan is equally valid--especially if he's available for cheap and LaRoche is going to be out for most of the season (and if the scouts haven't seen anything that indicates he's fallen off a cliff this year).