old t2.micro VS new t2.micro (same type!)

There isn't an old and a new t2.micro type, they are the same type.

New generation instance would be a t3.micro (read about the t3 family)

If you are looking to modernize, you should move to the t3 family from the t2 family. If you are able to migrate your workload to ARM, then have a look at the t4g family.

Price wise, in US regions a t2.micro is $0.0116 per hour on-demand and a t3.micro is $0.0104, so the t3.micro is 91% the price of a t2.micro. Other than being a newer instance type, the t3 family has more predictable burst characteristics than the t2 family.

To learn about burstable instance types read: https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/burstable-credits-baseline-concepts.html

For additional savings look to the t3a.micro for $0.0094/hr in US regions. Same CPU/memory as the t3.micro but based on AMD CPU rather than Intel.