Talk about engine building here. New products, tricky questions or showcase your work - If it's engine building related it's welcome here.
The stock compression ratio is around 12,5 : 1
So there might be a lot of dependencies, but if I installed pistons with a 14 : 1 compression ratio how much would that effect power?
I was also thinking of getting bigger pistons too...
Going to depend a LOT on the fuel you're going to be using and the camshafts you're intending to use - it is also rather expensive and time consuming.
You could gain a couple of percent or lose a bit more if you have to compromise timing, there are bike specific forums that could help you more. BTW, the CR may be 12.8:1 for that version?
An over-bore would be more useful, especially if you decide to go for the higher compression, as you're already making the main part of the investment and it will give the best cylinder finish - assuming, of course, that it doesn't use a plated bore, OEM.
Been doing some checking, it seems there are a few things to bear in mind - quite a lot of reports of crankshaft breakage of the K9 (especially the early ones) at high (13k+) rpm, the catalytic converter tends to choke up and removal is recommended, Yoshi' camshafts*, etc. are recommended. http://44teeth.com/modifying-suzuki-gsx-r1000/
https://www.rcsperformanceonline.com/Gsxr_1000_Stroker_Piston_Kits_p/je-stroker-pistons-gsxr-.htm - they only list the earlier versions, but may be worth talking to - their stroker cranks are welded and reground, though...
https://www.carpenterracing.com/sbp_gsxr1000-0104.htm - ditto, but a 'phone call wouldn't hurt.
https://gsxrzone.com/cranks.html - these guys use billet cranks!
The word on GSX-R1000 engines around then was the cranks were fragile when they were road raced with the OEM Alternator/Flywheel.
The ASBK Superbikes I worked on back then all ran the Yoshi Alternator and never had an issue with cranks.