War and Game

The Heinkel He-112 arrived with Legion Condor, with the Bf-109. This was for experimental purposes (V3, V4, V5). Some Spanish pilots tested the He-112V and found it underpowered. 

 
The main sources say that, later, a total of 15-20 He-112B arrived to Spain between December 1938 and January 1939 and formed the 5-G-5 fighter group with Spanish Pilots, coded from 5-51 to 5-67.
 
After WWII these aircraft were little used in operations, because lack of supplies, so I think they were scrapped on late 1940's and early 1950's with the Bf-109s which survived the Spanish Civil War.

He 112 saw actual combat during Spanish Civil War and as far as I know no problems were experienced with the fighter's armament. Some pilots in fact preferred He 112 to Me 109. The former had much better handling on the ground, offered its pilot a better visibility and, due to lower wing loading, was more maneuverable.

He 112 vs. Bf 109

In the initial trials, the early He112A prototypes were heavier than and inferior in performance to the 109. There can be little doubt that the correct decision was made, at the time. Heinkel then refined the design to the He112B, which was lighter and by some accounts a nicer aircraft to fly than the 109B/C series, with similar or slightly better performance. By then the 109 was being developed for the more powerful DB601 engine. Attempts to modify the He112 with this engine were basically unsuccessful.

Given a better start, then perhaps the He112 could have proven an equivalent fighter to the 109 or even slightly better. Or perhaps not. However, the Luftwaffe did not lose the Battle of Britain because of the quality of its main fighter.

Unfortunately, there was never a level playing field between these two aircraft. Heinkel had to maintain a wingloading of less than 100 kg/square meter, build a double-sparred wing, and retain an open cockpit. At least one source also mentions the need to provide for storage of four light bombs. Messerschmitt himself states that he was given a clear slate in designing his aircraft, although Kosin says that he was limited to a wing loading of less than 125 kg/square meter. Heinkel's chances were not helped when the designers kept piddling around with the details of the aircraft. Yes, the 112 was all curves, but so was the Spitfire, and a German study in early 1941 -- which I mentioned some time ago on this site, and others -- showed that the Spitfire, using current German technology, took less than 5% more hours to build than did the 109, for the 1000th aircraft.

The various requirements resulted, obviously, in a larger aircraft for both Arado and Heinkel. So, the 109 would be faster and have a better climb rate, which it did. But, the 112 had a better turning radius, although I don't know if this was tested for. The 112 was an easier plane to fly, especially after it had been slimmed down and simplified somewhat. Falck's unit was assigned to the 112 for a time and loved it -- and was saddened when it needed to return the 112s for 109s. And, the 112 had better development possibilities than did the 109. The 112 wing was able to mount both a 20mm cannon and bomb racks totally internally. Meanwhile, the 109 had not been planned for any use of the wings except to support the aircraft. So, extraordinary means were needed to mount the ammunition for the wing-mounted machine guns -- a loop going from wing root to wing tip. When the cannon were first mounted in the wing, the only thing keeping the wing spar from buckling from the recoil was the rivets securing it to the wing upper and lower panelling, and rivets popped all around the spar mounting. And, as for engine mounted weapons, the early 112 was able to mount a 20mm cannon to fire through the engine spinner, while the 109 wasn't even able to successfully mount a machine gun in that position.

Now, I don't know if the Battle of Britain would have been affected by having the 112 instead of the 109, but I really don't think it would have ended any worse than it did. The best solution would probably have been to permit development of both aircraft, certainly all other wartime nations had provided for this.

I detailed the topic in my book on the He 112, published by Squadron/Signal, in their 'In Action' series.
Besides the He 112's qualities listed by the previous posters, we should also mention the all-around cockpit visibility for the 'B' series, as well as the robusteness of, and wide distance between, the main landing gears, which would have certainly reduced dramatically the number of landing and taxiing accidents the Bf 109 was notorious of.
However, the He 112 was more time and resource-consuming to be built, and the Luftwaffe could afford neither.

From Ernst Heinkel's "Stürmisches Leben", I got the impression that the He 112's development wasn't quite finished yet when the Luftwaffe decided on the Me 109.

Willy Messerschmitt in the 1960s (I believe) was interviewed by the news magazine "Der Spiegel" and explained that he didn't like the fighter design goals of the RLM. He argued in favour of top speed being the priority goal: "And when the 'Schnellbomber' (term for the new tactical category 'fast bomber') arrives, then what are you going to do?" Apparently, the RLM followed his logic and went with his priorities.

Heinkel included the following comparison between He 112 and He 100 in "Stürmisches Leben":

"While the He 112 required 2885 individual [HoHun: different] parts, the He 100 at a later stage only needed 969. Instead of 26964 rivets the He 100 required only 11543, and the number of normed parts had risen from 1279 for the He 112 to 2186 for the He 100. By the savings in rivets alone the time necessary for building the wing was reduced by no less than 1150 man hours. Additionally, in areas difficult to access for riveting with conventional measures we had previously frequently abandoned light-weight construction techniques, but now we had applied a new technique using explosive rivets developed in Marienehe by two of my engineers, the Butter brothers."

I assume this is an implicit admission that the He 112's production efficiency was inadequate. While Heinkel goes into great detail on the failure of the Luftwaffe to adopt the He 100, he devotes very little space to the He 112 vs. Me 109 competitions. I believe this might be another indication he didn't really disagree with the Luftwaffe on the relative merits of both fighters.