As the payment is made in connection with your job - it is considered a compensation for your service and - yes - it is taxable income. If you receive W2 form - the payment should be included in your wages and reported in the box 1.
However for whatever reason the company decided to use 1099-misc form. You may communicate with the payroll person asking to correct. Otherwise - you would need to report that income on the schedule C as self-employment. You would be able to deduct qualified expenses related to your job - that will reduce your net self-employment income that is a subject of self-employment taxes.
In additional - you may deduct your moving expenses. Please see IRS publication 521 for details - http://www.irs.gov/pub/irs-pdf/p521.pdf
accounting dept. said I was in a better tax position by filing the 1099 then the W2. Is that right?
Yes and No. You may use the situation for your advantages, but it is not comes automatically.
If you have any expenses related to your job - such as tools, special clothes, licenses, etc - you may deduct them on the schedule C. As an employee - you also may deduct these expenses, but you should itemize and would be limited by 2% AGI floor - so in most situation you do not benefits from these deductions as an employee. There is no such limitation for self-employed - and you may greatly benefit.
If you do not have any job related expenses - assuming the amount paid would be the same - you would end up paying self-employment taxes 15.3% instead of 7,65% FICA tax. In additional your tax return will be more complex (and cost more).