No reason, provided you confidently expect to be out of the house in 5 years or less. If your time horizon is longer, the choice becomes more difficult, but the ARM remains the better choice if you manage it properly. Managing it properly means being prepared to refinance the ARM at the end of 5 years.
The balloon is the simpler instrument of the two. The word "balloon" means that there is a balance at the end of the term that must be repaid. In the 1920s most balloon loans were interest-only, meaning that the borrower paid interest but no principal. At the end of the term, usually 5 or 10 years, the balloon that had to be repaid was equal to the original loan amount. The balloon loans offered today, in contrast, calculate payments as if the loan was going to be paid off completely over 30 years. Assuming a rate of 6.5%, for example, a $100,000 loan would have a balance remaining at the end of the fifth year of $93,611.
Unless you come into a sudden bequest, the balloon at the end of 5 years must be repaid with the proceeds of a new loan, and you will pay some settlement costs in the process. In contrast, the interest rate on a 5-year ARM resets using a mechanical rate adjustment procedure. This procedure is spelled out in the original contract, which remains in force, so there are no added settlement costs. This is an advantage of an ARM but only if the ARM is not refinanced.
A more important advantage of the ARM is that the initial rate is generally lower than the rate on a balloon with a comparable term. This is the case with the loans offered to you. If you sell your house or refinance within 5 years, you clearly do better with the ARM.
A third important advantage of the ARM is that it provides valuable protection against a future interest rate explosion, which is unlikely but could happen. Between 1977 and 1981, for example, mortgage rates increased by about 9%. If that experience were repeated, the rate on the balloon would rise to 15.5% and you would be saddled with refinance costs, but the rate on the ARM would go only to 11.125%, which is the maximum rate on that ARM, and there would be no refinance costs.
The drawback of the ARM is that, in the absence of an interest rate explosion, the rate will reset substantially above the balloon rate. If market rates do not change over the 5 year period, for example, you could refinance into another balloon loan at 6.50%, but the ARM rate would jump to 8.25%. This is calculated as the value of the one-year Treasury index which was 5.39% in April, 1998, plus the margin of 2.75%, or 8.14%, which is rounded to 8.25%.
The low initial rate on the ARM is a "teaser" designed to produce much higher rates down the road. The ARM lender is betting that interest rates will not explode, and that you won't refinance when the 5-year adjustment date approaches. You foil this scheme by doing exactly what you would be obliged to do on a balloon loan; you refinance at the end of the 5 years. By refinancing, you again get the benefit of the preferential rate offered on the ARM for the initial 5-year period, and it is no more costly to refinance the ARM than the balloon. If interest rates have exploded, on the other hand, you stay put, save the refinance costs, and count your blessings.
Postscript
When the above was written, the ARM was clearly the better choice because it had a lower rate and lower risk. Since then, however, the market has eliminated this anomaly. A 5-year balloon now has a lower rate than a 5/1 ARM, but it continues to have greater risk in a rising rate environment. This makes the choice more difficult.