Calcium batteries are fine if it is for starting only. DO NOT use calcium if the battery will be cycling, ie discharging without engine running as in a house battery application in a motor home. We have problems where calcium batteries have been fitted in trucks with tail gate lifters, or vehicles with rt's, computers scanners, etc that are left on all the time. The batteries need a higher charge rate than a standard lead antimony battery, and need to gas for longer to avoid stratification. Modern alternators will charge up to 14.5v, which is ideal, but earlier alts that peak at 14.2v struggle to maintain a calcium battery if it has any extra discharge beyond ordinary automotive use. To make matters worse a lot of modern cars have pcm controlled regulators, where the computer decides how much to charge the battery, and takes control of the alternator once engine temp is up. The worst case we've found so far is the Aussie BF Falcon which starts charging at 14.2v or higher, but within 20 min is struggling to put 13.3v into the battery, regardless of electrical loading. Antimony batteries last for 3-4 years, but the calciums are struggling to get 18 mths. I have one customer had 4 batteries in a car that was first used Jan 2008. His previous car had constant battery problems. The Holden Commodore had similar problems, but GM had the brain capacity to recalibrate their ecu, but Ford won't recognise the problem.
The main sales pitch from battery manufactures for calcium batteries, is they withstand the higher engine bay temperatures in modern vehicles better than antimony batteries. Also their shelf life is longer, before natural discharge, which suits shops that have stock sitting for long periods.
If you put a bigger battery in than manufacturers specs, it won't necessarily start the engine any faster unless you have an existing fault like glow plug fault, but it will last longer before going flat if something is left on, and also will take longer to recharge. Not necessarily negatives, but something to be aware of.
Make sure you have the battery tested, check charging, and check for leakoff or discharge before buying a new battery. This should be under 40mA on most vehicles, anything over 100mA you need to have an auto electrician check the cause of the leakoff.