The rode nt1 is a professional quality dynamic microphone with an on/off switch and designed with the performer in mind.
It has a tailored frequency response that makes it effective for miking guitar cabinets, drums, cymbals or any other application where bleed is an issue. It’s also popularly used as an all-purpose vocal microphone.
The rode nt2a is a professional quality large diaphragm condenser microphone that offers fixed cardioid and omni pattern settings. It has a wide dynamic range, low self-noise and provides high sensitivity with no distortion.
There are few differences between the NT1 and NT2a:
NT1: only 1 polar pattern to choose from (cardioid) NT2a: two different polar patterns to choose from (omni and cardioid) NT1: on/off switch is not required since it’s always “live” NT2a: requires phantom power to be turned on.

Due to the large diaphragm, the rode nt2a offers a more detailed sound, but its cardioid polar pattern makes it less sensitive to room ambiance.
The NT1 has many uses including live vocal performances, home studios and broadcast applications. It can be picked up for about $150 used or for about $300 brand new with the warranty.
The NT2a is usually picked up for $1000 and up used or for $1300 and up brand new with the warranty.

The main difference between these two mics is that the NT1 is made with a fixed cardioid polar pattern which means it’s not as sensitive to the environmental ambiance, so it may be more ideal for live performances where there is most likely going to be loud instruments on stage.
The NT2a is made with an omni polar pattern, which means it’s more sensitive to environmental ambiance and may be ideal for studio recording or broadcasting because there will be no “proximity” effect which occurs when the source is too close to the microphone.
NT1: not as detailed sound , but still excellent quality NT2a: more detailed sound , but not as perfect for live shows.
Both of these microphones are extremely popular and they both do their job very well. It all comes down to budget, specifications and personal preferences.
For the same price, the Rode NT2a is probably your best bet because it offers better quality than the NT1 and it offers more polar pattern options than the NT1.
However, if you’re working with a limited budget, the NT1 is still an excellent microphone that will provide great quality for live shows or studios!