I reread your question several times as I wanted to be certain as to the answer you are looking for. You asked "How do I think about buying term llife insurance vs. whole life insurance". Christopher's answer addressed this question, but the other two did not. You didn't ask "should I buy" or "is whole life insurance a good buy". So here is how I work with clients to answer this question. We can't cover all the considerations due to space limitations here. I will try to hit the major points.
First and foremost, if you are looking at life insurance to protect loved ones or a business interest, you need to purchase the proper amount of death benefit to protect those interests. Most folks buy far too little death benefit and their beneficiaries find out too late that they still have hard choices to make. You should find out what the maximum amount of coverage that the company will issue based on your circumstances. Companies will not sell you an unlimited amount of coverage, just the amount that is economically justified by your age and financial standing. No insurance coverage will pay you more than the risk is worth. There is too much incentive for someone to commit fraud in order to make a profit and that is why you cannot buy "too much" coverage from a reputable company" only the amount that can be justified through underwriting. Now that you know that amount. Decide what you want the coverage to do by answering this question: "If I died tonight, what do I want to happen to my family (business) tomorrow?" So if you have a non working spouse and 3 young kids, what do you spend a year supporting them? Do you want them to go to college and when? Do you want to pay off the house?, etc. Then you decide if you maximum coverage amount is too high based on your objectives and adjust down accordingly.
Here are the considerations as to which to buy. Do you have enough money or income to pay the premium. As the others pointed out, you write a smaller check for the term insurance than the whole life alternative. If you have limited funds, then the decision is made for you. I would, however, pick a term insurance product that is fully convertible, to ANY permanent product that the company offers. I can't emphasize how important this is. If your health changes and you can't replace the term coverage when the level premium period expires you will definitely want to exercise your conversion option. Companies who limit your conversion choices usually provide relatively unattractive permanent policies to those wishing to convert.
The next consideration is how long will I want the coverage to be in place? Life insurance is unique in that it is the only insurance product that insures something that is GUARANTEED to happen! We are all going to die. Usually if the coverage is desired for more than 10 years you will be economically better off with the whole life product when looking at the total "net economic cost" which is the cost of term plus the "lost opportunity cost" for the insurance. (That is the amount you would have earned on the money had you invested it instead of sending it to the insurance company).
Third is your overall financial plan. There are many ways to structure a whole life or other permanent policy (not a variable universal life though, that is different) to generate lots of cash value in the early years. It requires someone who understands the tax code and various insurance policy contract provisions in order to do this. Most agents and financial planners don't know how to make this work, so ask if they have experience with policies that will perform this way and what part of the IRS code they need to understand (sect 7702). I have clients who use this tool as an alternative to investment grade bonds. You get a better guarantee of principal, generally higher interest rates earned, compound instead of simple interest, and the book value actually goes up if interest rates rise (a bond will lose value if that were to happen). You enjoy guarantees of principal every day you own it unlike a bond which is only guaranteed to have it's full value on the day it matures. Others use it instead of a bank savings account or money market fund. It pays far more interest, is very liquid and enjoys tax deferred growth with tax free access options to use the money in the policy when you are alive.
This discussion could go on much farther covering how to use the policy to be your own banker, provide lower car and homeowner's insurance costs and a variety of other benefits. I hope this discussion helps you in evaluating your options.