Air Arms S510 Carbine or Brocock Compatto .177?

Both the Taipan and AA have better triggers than the Brocock.

Agree with this. The Brocock trigger is definitely not bad, but in my experience just can't be adjusted as nice. Maybe could be if internal work is done, but that is not my 'thing.'

I don't like the 't-mount' fill probe on the AA's, but that is a minor gripe (and can be changed out to a standard Foster male with parts from BestFittings UK).

Daystate Huntsman Revere would be another rifle of the same type I would look hard at.

Or a used Wolverine when they come up on a site like AOA's 'pre-owned' page. My wife also has an FX Dreamline Classic in black pepper lam stock (.22 cal though), and I can't fault that rifle one bit.
 
They are both very decent rifles, but if I wanted something short, I'd pick a Taipan Veteran over both of them. I've owned all three, and the Veteran is sturdier, simpler, easier to tune and adjust. Both the Taipan and AA have better triggers than the Brocock.

100% agree unless you don’t want a bull pup. I have a standard and HP Daystate Pulsar and the Taipan build quality is better. I know some don’t like the rear cocking but the tolerances on their system is amazing. I don’t see how they could replicate it moving the lever forward and that’s why I would prefer them not to do this or offer two different models. It’s also going to be much quieter than those other two due to the larger shroud they use. If you only want to consider the two you listed I would buy the Brocock over the AA but that’s only preference to me as I like the semi bull pup design better . They are both fine rifles though so there isn’t a wrong choice between the two. 

 
Had both a Compatto and a Regal.....both are incredible shooters. In the field, I took the Compatto every time as the ballistic nylon stock is built for that terrain, the Regal's beautiful walnut stock I did not want to scratch! LOL! You couldn't go wrong with an AA, solid rifles. You're only going to get 30 shots from the Compatto fyi, 45 with the Regal. You'd get more shots with a Taipan.
 
My friend has a Compatto in .177. My Taipan is an absolute club compared to it so I understand the appeal of something not so weird. What I really like about his Compatto is offhand shooting. One of the nicest guns I’ve ever shot offhand. The only thing that made him mad about the gun is having such a nice gun in a plastic stock. Last time I talked to him he said he was going to duplicate that piece of plastic out of walnut. 
 
Of the two guns you asked about...The Brocock is a very comfortable gun, fast and light. My son started shooting it when he was 7 and it was perfect for him, a blast to shoot. It’s super accurate, quiet and smooth. We sold ours for one reason...the trigger. My wife has an S510 and it’s also comfortable, obviously a more traditional feel, very very accurate, quiet but the trigger is much better. 
You can’t go wrong with either!

Stoti
 
I like the Compatto better than an AA 4xx/5xx carbine feels better and lighter to me when shouldered and very nice thin forend to hold and the Brockock is naturally quieter. Trigger is not bad after its broken in. They are pretty terrible when brand new though.

I like the Daystate Regal XL better though for traditional rifle shooting.
 
I can’t comment on the Brocock guns, since I’ve never shot one. But I do own Air Arms 410 and Daystate Hunstman Regal. They are both great guns, neither is pellet fusy and both are Lasers. I’ve had My Air Arms-long time and have dispatched a lot of critters with it. If I was in your shoes I’d take the Air Arms, but those 3 rifles are all good, either one you’d be happy with. 👍🇺🇸