Although (arguably) use and utilize have the same denotation, their connotations call for differing usages. Both mean "to put to practical purpose." However, utilize is used when something is used for a purpose for which it was NOT designed. For example:
Quincy used his credit card to purchase 25 copies of Moby Dick.
Quincy utilized his credit card to pick the lock on his front door when he forgot his key.
Utilize also connotes making use of something in a mechanical or scientific way.
If you'd like another perspective, here's what Grammar Girl has to say on the subject:
Bonnie says that as a copy editor she often reads fluffed up marketing material full of big words that try to make the writer sound important or knowledgeable. She usually just changes them
to normal, unimpressive words that get the point across without much fuss. One of these words she changes often is “utilize,” as in the pretentious-sounding sentence “If you utilize this brand of printer, you will go far.” A sentence like that sounds fluffy and overly important, and it gives readers the impression that you’re trying too hard. Most of the time you can avoid the verb
“utilize”; “use” works just fine (7).
So if you’re in marketing or PR, you can just use “use”; it’s probably not a good idea to utilize “utilize.” In a similar vein, please avoid the word “utilization.” It does your sentence no
Surprisingly, “utilize,” a 19th-century loanword from French (8), does have very specific and valid uses, mostly in the scientific world. The word “utilize” often appears “in contexts in which a strategy is put to practical advantage or a chemical or nutrient is being taken up and used effectively” (9). For example, according to the American Heritage Guide to Contemporary Usage and Style, you might hear “utilize” properly used in a sentence such as “If a diet contains too much phosphorus, calcium is not utilized efficiently” (9).
So if you're a science writer, you might find yourself using the word “utilize.” If you’re just a regular person writing a regular sentence, you should probably just stick with the word “use.”