Although the "hardware" specs look similar for the T2.medium instance and the M3.medium instance, the difference is when you consider Burstable vs. Fixed Performance. See this link from Amazon Web Services:
http://aws.amazon.com/ec2/faqs/#burst
The following quote comes from that link:
Q: When should I choose a Burstable Performance Instance, such as T2?
Workloads ideal for Burstable Performance Instances (e.g. web servers, developer environments, and small databases) don’t use the full CPU often or consistently, but occasionally need to burst. If your application requires sustained high CPU performance, we recommend our Fixed Performance Instances, such as M3, C3, and R3.
A T2 instance accrues CPU credits, but only as long as it runs. If it is stopped or terminated, the credits accrued are gone.
There is an important piece of information further down the page concerning the CPU credits for the T2 instances:
Q: What happens to CPU performance if my T2 instance is running low on credits (CPU Credit balance is near zero)?
If your T2 instance has a zero CPU Credit balance, performance will remain at baseline CPU performance. For example, the t2.micro provides baseline CPU performance of 10% of a physical CPU core. If your instance’s CPU Credit balance is approaching zero, CPU performance will be lowered to baseline performance over a 15-minute interval.
This means if you run out of burstable credits, your performance will be limited to a fixed percentage of a single core until you accrue more; 10% for T2.micro, 20% for T2.small, and 40% for T2.medium.
Another important difference that the OP mentions is the M3.medium instance can be provisioned with 4GB of ephemeral storage, which has much greater I/O capacity than persistent, Elastic Block Storage (EBS). T2 instances do not have this option.
Finally, it depends on what a "hit" is. In my opinion, if a hit means a few static page downloads that are less than 64k or small dynamic pages, then I'd explore the T2 option. For longer sessions, more data traffic, or higher numbers of concurrent users, I'd consider the M3. And if performance over an extended time period is a key issue, I think you're definitely in M3 land.
Look at the logs for your present site or a site similar to what you're setting up and determine which situation you're in.