In her book Horrible Words: A Guide to the Misuse of English (2016), Rebecca Gowers uses the word gripers in preference to sticklers (a word I myself always associate with Lynne Truss’s famous Eats Shoots and Leaves), and in her paper at our Life after HUGE? symposium in December last year, she explained why.
Force of habit made me check the word in the OED just now, where I found only two quotations for griper, n., sense 7, both from the 1930s and both from an American source (the same one). The entry has not been updated yet (and it will be interesting to see whether Rebecca’s use of the word makes it into the OED when it is!), but it did make me wonder whether griper in the sense “One who complains” is indeed an Americanism. Is it?
Bridging the Unbridgeable 
My Chambers (13th edition, 2014) lists “griper” without a label, as does the Concise Oxford (11th edition, 2008) and Webster’s Ninth New Collegiate (1983), so perhaps it isn’t. Once again, more to be done …
Here are some figures from the Google Ngram Viewer (If it’s good enough for Bryan Garner …):
gripers vs. sticklers
Google Ngram Viewer
1800–2000
English corpus
1800
gripers 0.0000006990
sticklers 0.0000153278
1900
gripers 0.0000000568
sticklers 0.0000138363
2000
gripers 0.0000003263
sticklers 0.0000039619
American English corpus
1800
gripers 0.0000000000
sticklers 0.0000023241
1900
gripers 0.0000000418
sticklers 0.0000118947
2000
gripers 0.0000003895
sticklers 0.0000044189
British English corpus
1800
gripers 0.0000013653
sticklers 0.0000189870
1900
gripers 0.0000003685
sticklers 0.0000114812
2000
gripers 0.0000001480
sticklers 0.0000031850
This would seem to suggest that, even given the limitations of the corpus, “stickler” has been the more common term for two centuries in both British and American English.
Merriam-Webster Collegiate (1959) labels the verb gripe in its sense “to grumble; complain” as US slang
FWIW, GloWbE has nine genuine* hits for ‘griper’/‘gripers’ in the US section, versus three in the GB one and one in AU. The term is not attested in any others.
* In the GB section there are 16 spurious hits involving the (rare) surname Griper.