Not trying to sway people either way C of A or LAA you like what you like.
I have an absolute beut of an RV6 with a IO360 superior engine with 1 mag and 1 electronic ignition runs sweet. It also has an MT 3 blade wobbly on it so quite a complex aircraft for a LAA type but there's plenty of them. I bought off the previous owner 1 year old and 40 hours on it. He was just a compulsive builder, already building his next project.
For my aircraft you have the 3 logbooks, engine,prop, and airframe. If work is done outside of pilot maintenance then my inspector checks and signs it off via worksheets these are referenced in the logbook. Sounds a lot but a doddle really.
A friend of mine has a mooney and just installed a new Garmin mode S and cost him over 3G. I have just had my AT 150 replaced with the same mode S and had it installed by a certified avionics guy and cost me £1600. The LAA didn't charge anything for the updated paperwork. My avionics guy also has different rates for LAA and C of A.
I done my permit renewal with my inspector at the same time giving the aircraft a service, total cost was about £300.00
Do remember though LAA are limited to day VFR only. I'm not trying to say one type is better than another it's all about what you fancy flying.