The MT program is more in depth than MLT programs, by and large, but this is debatable since the majority of your expertise comes from on-the-job experience rather than education. I am a CLS student so take that for what it's worth. The big difference is pay. Salary for MLT's is around 25-40k/year, for MT(ASCP) around 45-60k. Only MT's can become supervisors and lab managers. In states that have few standards, MLT's and MT's can perform the same testing. Some states that issue licenses, such as California, limit MLT's to basic lab procedures, relegating medium- and high-complexity testing for MT's. MLT's are able to sit for the MT(ASCP) exam if they have a B.S. and 2 years of experience.
You should also understand you cannot sit for the ASCP exam simply because you have a BS in a science. You must first complete an accredited program. For more certification, see the ASCP website: www.ascp.org/Board-of-Certification/GetCertified#tabs-1