HKs have a very loyal fan base (often referred to as HK Snobs) in a joking manner to reflect the high cost of HK firearms, especially when comparing similar pistols from other manufacturers. Sigs also their own loyal users, which is probably larger than HK but slightly less fiercely loyal.
Both companies are German and produce excellent firearms. The Sig P226 is an excellent example and is used by both police and military forces around the globe. They are known for being very solid, robust, all or mostly metal, as well as reliable.
HK also has a reputation for very reliable, well built with extremely precise manufacturing tolerances, as well as reliable. Uncommon to popular belief H&K produced the world’s first polymer handgun – not Glock. I would say Glock did as Apple with the cell phone market by revolutionizing an already existing product type vs re-inventing the wheel.
But again in regards to HK and Sig, I would be perfectly comfortable and happy with either one. Reliability, as previously stated as well as accuracy, and consistency are key factors adding to their success.
While the most popular Sig models are mostly full size handguns, HK offers a variety of popular, high demand handgun sizes. Their USP line which originated in the 80’s is still very popular today and offers full sized and compact frames. The successor to the USP compact, the HK P2000 recently found it’s way into the holsters over 26,000 federal agents in and around 2014/2015.
Lastly in regards to recoil, I would have disagree with the other posters answer just a bit. While Sig controls recoil solely by the heavy weight of the firearm (general rule of thumb is the heavier the gun, the less the felt recoil), HK actually builds special recoil reduction devices into a majority of their smaller handguns.
For instance a sub compact, the P2000sk (the smallest HK one can buy) shooting the usual “snappy” .40 S&W round had a significantly less felt recoil vs the much larger, heavier and full framed Sig P226. This was noticed by myself and several other shooters and was quite surprising given how much smaller the P2000sk is. Now while this test was by no means scientific and or measured with instruments, it was very easy to notice and agreed upon by all participating shooters.
To sum up both are two very outstanding German based companies with excellent track records. However my personal opinion/feelings regarding the two is that HKs have more of a “sexy,” highly appealing aesthetic design factor which drives the “coolness” factor but also proven reliability, adaptability for all shooters. Sigs run and run and then run some more with more focus towards extreme reliability and toughness.
So short answer is neither is better. They are both excellent and you should try shooting both at a range. While they may seem similar given the fact youre comparing them in your question I’d say being of German origin is the only thing they have in common.