The only reason I mentioned the French accent was that there are parts of Brahms's 4th Symphony (my favourite Brahms symph) that could almost have been written by Berlioz (in his quieter, introspective moments). Nothing huge or outstanding, but just a motif here or a change of texture there, but enough to make me think there was a little less of a German quality and a little more of a French quality. There are also parts of the German Requiem that do the same for me.
Also, the only point I was commenting upon was whether it was LvB or Brahms that moved the Classical era into Romantic. I too do not think that there are that many similarities between the music of these two composers, and largely for the same reasons JHC has outlined above - although I would not personally call Brahms's music "muddled". Brahms's orchestrations usually tended to be "safe" whereas LvB was always willing to push things.
LvB was also often a lot more adventurous with his harmonies (in context that is - it may not sound adventurous compared to the sorts of harmonies heard in the times of Brahms, but in context of what was the "norm" in the Classical era, LvB was often pushing it. Remember that some colleagues unkindly thought LvB had completely lost it when he started the Allegretto mvt of his 7th with an inversion!).
Brahms was born 6 years after LvB's death so there was no overlap as there were with other composers in history (ie, one well-known composer knowing, meeting or being taught by another well-known composer). However, knowing that Brahms was a big fan of the likes of Bach and Beethoven, it's inevitable that he would "inherit" an affection for form and structure. Personally, I think that was really all he inherited though. Some of Brahms's harmonies are conservative even by Classical standards, let alone Romantic standards (which I find a little odd given that Brahms was so favoured by Schumann).
If Brahms "bridged" anything, for my ears it was the use of counterpoint. From the precision usage of it by Bach through to the often convoluted usage of it by Wagner, Brahms (I think anyway) sits in the middle, putting it nicely into his quite certain structures and relatively conservative harmonies.
I realise I've possibly overused the word conservative, but all in all, I don't think Brahms is any less deserving of his place in history than most others (I'll still prefer him over the likes of Mendelssohn or Wagner - but my "go to" Romantic composer will forever be Berlioz
).