I'm not familiar enough with the proofs to say if they are more than superficially different, but here is something:

[Moeglin-Waldspurger][1] prove continuation crediting Jacquet (see p. xix), instead of Langlands. They say it is similar to that given by [Efrat][2], in his treatment of the Hilbert-modular ($PSL_2$ over a totally real field) case. [Here][3], Jacquet credits M-W's proof to [Colin de Verdière's][4] "new and strikingly brief and elegant proof" (from the MR review) for $SL_2({\mathbb R})$ (extended [here][5]). I couldn't find any extensions of Colin de Verdière's argument to higher-rank cases, but that may be because it was done in Moeglin-Waldspurger.

[Muller][6] also has a proof in the rank-one case. 

[Wong][8] gave a proof using integral equations.

Everyone listed credits Selberg with their ideas.

  [1]: http://www.ams.org/mathscinet-getitem?mr=97d%3A11083
  [2]: http://www.ams.org/mathscinet-getitem?mr=88e%3A11041
  [3]: http://www.ams.org/mathscinet-getitem?mr=98k%3A11063
  [4]: http://www.ams.org/mathscinet-getitem?mr=83a%3A10038
  [5]: http://www.ams.org/mathscinet-getitem?mr=84k%3A58222
  [6]: http://www.ams.org/mathscinet-getitem?mr=98f%3A11053
  [7]: http://www.ams.org/mathscinet-getitem?mr=58%3A27768
  [8]: http://www.ams.org/mathscinet-getitem?mr=91c%3A11031