Bf 110s were not shy to enter an air combat during the BoB, and came from it with a positive kill/loss ratio, that was between the ratios of Spitfire and Hurricane. That is despite the disadvantage in raw performance vs. Spitfire, and the modest number of 110s used when compared with with how many 109s were used.
Which reference indicates the Bf110 more than held its own in fighter combat over Britain in 1940?
Using the Narrow Margin (Wood and Dempster) Figures the Luftwaffe reported its Bf110 force lost 224 on operations, 11 on operations not due to enemy action and 17 not on operations, July to October 1940. The Luftwaffe Claims list is nearly complete, the ZG and LG(Z) units claimed 233 kills July to October 1940, 1 Blenheim, 71 Hurricane, 161 Spitfire but 20 of the clams were not accepted. This is out of 2,216 claims known to be lodged by the JG, NJG and LG units.
August 1940 fighter combat loss figure is 338 RAF versus 177 Bf109 and 114 Bf110 (total 291), and in September, 358 RAF versus 187 Bf109 and 81 Bf110s (total 268). Gives 696 RAF to 519 Luftwaffe or 1.34 to 1. The ZG units claimed 225 kills against their 195 losses, including some unaccepted. If the ZG units really did shoot down more than they lost say, 1.1 to 1, or 220 actual kills that leaves the Bf109 units with 364 losses against the remaining 468 RAF fighters lost, some of which were lost to bombers. If you assume 10% of RAF losses were to bombers, that leaves around 400 fighters shot down by Bf109 or around 1.1 to 1, or the Bf1110 by virtue of its superior range was the better fighter, or the worse as it had more crew and engines etc.
The number of RAF fighters lost is fixed, the better the Bf110 is reported the worse the Bf109 becomes.
Stephen Bungay in his book The Most Dangerous Enemy has a break down of RAF losses 10 July to 11 August 1940, of the 115 combat losses 87 were to Bf109, 6 to Bf110, 13 to Luftwaffe bombers, 4 to collision, 1 to flak, 1 to friendly fire and 3 to unknown causes. Of the 106 damaged RAF fighters 52 were due to Bf109s, 38 by bomber gunners. In this time period the ZG units lodged 26 claims, while losing around 22 to RAF fighters.
In effect 13% of the fighters hit by bomber gunners were shot down, compared with 62% of the fighters hit by Bf109, half the pilots in the fighters hit by Bf109s were killed, compared with 10% of the fighters hit by bomber gunners. The Bf109s hit 63 Hurricanes, 63 Spitfires, 6 Defiants and 7 Blenheims, shooting down 45 of the Hurricanes, 31 of the Spitfires and 11 of the Defiants and Blenheims. The bomber gunners hit 25 Hurricanes and 25 Spitfires, shooting down 11 Hurricanes and 2 Spitfires. In all 51 Hurricane and 25 Spitfire pilots were killed. A number thanks to inadequate air sea rescue.
When it came to RAF firepower around 70% of the bombers hit were destroyed, for Bf109s it was 77% of those hit destroyed.
289 Bf110s and 934 Bf109 deployed against Britain as of 10 August 1940, making the force 23.6% twin engine.