Constant 1 G acceleration requires three things:
1. An infinite power source
2. A reactionless drive
3. A spacecraft made of material so strong that it can survive collisions with rocky material at velocities very close to c. Or a Star Trek style deflector shield.
Warp drive is probably easier to achieve.
Detonating nukes behind your spaceship will never give you anything close to 1G constant acceleration over a long period of time.
Time dilation has some definite drawbacks as well. Say for example you have a very redundant ship that can repair damage from micrometeorite attacks in a few minutes. The hits are very rare, maybe once a year at most at normal velocity. But now you're traveling at a high fraction of C and you're hitting tens of fragments per second, and always at a high fraction of C. Your repair process is effectively working in slow motion and could very easily get overwhelmed. Without a sci-fi energy shield your spacecraft is ablated to death long before you get anywhere.