Short answer is "Not necessarily".
I have had both, but its been 20 years since I lived in a house with window units, but I have been working as an engineer in the commercial and industrial air conditioning industry for 30 years and get involved in these comparisons routinely. If you have a small portion of your house that you spend a lot of time in, you might benefit from window units or a "zoned" system by turning up the temp in the unoccupied areas of the house, something you can't do with a central system. The downside of doing this would be an increase in the temperature of room you only pass through, and an increase in the humidity of the house in whole (South TX, right?) Also consideration must be given to the efficiency of each type of system; a new 14 SEER system would cost the same to cool the whole house as an old 7 SEER system on half the house, regardless of system type.
Also, if you are considering the purchase of new air conditioning equipment, some of the major brands of central air conditioners are manufactured in Texas, Arkansas, and Tennessee. I believe you would find it difficult to find a major brand of window a/c is manufactured domestically. As much as I try to think globally, I like my neighbors to have jobs.
