1. 223 is good to 300 yards... in Nevada I used a .223 w/ a 40 gr bullet and with the savings (in 2009 .223 was CHEAP of course) PRACTICED, PRACTICED, PRACTICED...
2.Bobcats are small. A 10mph gust comes up you can make bad shot placement or miss. Get what you want, but load it slow (.223 40 grain down to 3250) or light (17 hmr 20 gr, 204 32 gr).
3.Excessive damage is not just the 22 or 25 caliber question. It's energy. Look at energy numbers. An old Winchester 25-35 with a 16" barrel with a 75 grain will make a single hole, because there isn't much energy.
4.You will get the fever when you know you fooled something as smart as a bobcat; it will destroy your accuracy. Most are smarter than the average human. They might come for food and get shot, but live in their shoes and they aren't doing to bad considering we've been trying to wipe them out for hundreds of years. Think about it, the Lynx almost died off. Not so with Bobcats. Coyotes? Remember that wolves weren't prevalent in the lower 48 for a almost 50 years until we brought them back and protected them. These animals didn't get wiped out because they didn't give people the ability to kill them easily. Most coyotes in hard hunted areas have learned, and only give in to instinct when they are assured of food. Even then they pause and look, multiple times. You need to make your shots go to the right spot, EXACTLY the right spot.
5.Every rifle is different. Same load, action, same McGowan barrels, trued by the same gunsmith, elevation, etc. They have different speeds, and flight characteristics. A rifle that shoots different means a different amount of speed, and therefore energy; and a different amount of doping for wind, drop, etc.Technology has improved this, but it is still prevalent.
6.Even with a custom built rifle you have to be able to read the wind, distance, slope, elevation, account for temp drop (air thickness; most people sight in their rifle at 45-70+ degrees and it will be 12 degrees when they go hunting), etc. Practice, Practice, Practice. Because if it was as easy as having money to dump in a rifle no one in my family would hunt coyotes very well. Or save the hide on a cat. My rifle and scope cost $275, and even with that [beeep] pos, I still have coyotes out to 200, 225 on a good down or uphill, 250 yards on a steep mountain at 10x. How do I use a 10X at 250 yards? Only in perfect conditions; some days I'd be as good off with a 22lr. Pick your equipment, bend your tactics to its strengths, and then minimize your disadvantages. What tactics work for you are yours and yours alone. That's all experience, from on the range to shooting outdoors at different elevations, etc., to hunting.