As to buying or renting, I look at how many times I will use it per year vs the cost of rental and the cost of purchase. Also factor in maintenance costs.
I was building a fence and needed an air compressor and nail gun. But I took a couple of months to build the fence. In this case, it made more sense for me to purchase the nail gun and air compressor. Then I could take my time building the fence. Also I use these for other projects.
In the case of splitting firewood and getting a log splitter, it costs $60 a day for rental and around $1400 to buy a splitter. I only need it two days a year and it could easily cost $25 or $50 just to fix it when needed. So makes a whole lot of sense to rent instead of buy in this case. Also stick $1400 in the bank at 5% interest and you would get around $70 a year.
Then think storage. Might not want to buy equipment you seldom use if you don't have much storage space for the equipment.