I have Springer that has the standard turn signal bulbs. Can I replace those 1157 and 1156 bulbs with LED bulbs? Who makes the best ones?
There are MANY (many many many many many) different LED bulbs in the 1156 or 1157 format. They'll have anywhere from a few LED segments to many. Have seen them with as few as three and as many as 32. And I know my look wasn't exhaustive. Differences in brightness also.
All that is to say you can't say "LED bulb" by itself anymore and assume there is any kind of apples to apples comparison.
Some of the bulbs are big because they've got so many lights stacked on them. Have seen some so large they won't fit in a Harley bullet housing. Easiest solution will be to hit your local full line auto parts store. They'll likely have some right there you can match size to. They'll likely also be a common or known branded product and have a local warranty you can handle right there at the store if you need to.
They'll be more expensive than the stuff that can be ordered online. And they might not be better. But they won't be bad. If you want to shop online try a known entity like Custom Dynamics.