Based on the lack of information, I'll make the following assumptions:
The old PSU was brandless, less than 450W (I would guess 250W), probably came with the case, and that this is an old computer.
The new PSU is probably also brandless, 450W, and is probably more than enough for an old computer.
If I am right, this is good, because it can probably only provide 400W of stable power (if it's brandless) which should be enough and therefor not make it likely to explode any time soon.
To my knowledge, the things that can blow up PSUs: Incorrect voltage (some have a voltage switch on the back... flip it and it will blow up - I've done it myself), cheap/damaged/flakey/badly-fitted power cables (rarely causes problems, but I've seen it a couple times before in houses with pets), overloading the PSU (using a weak PSU in a powerful computer, or just a PSU that doesn't produce the wattage it claims - common in brandless PSUs), overheating the PSU (common in any cheap PSU, but also in cases without enough ventilation... also caused by parts wearing out or dust inside the PSU creating static fields), and power surges (lightning~). Power up/down cycles also wear out PSUs, so eventually they will all blow up, but this hasn't been a real issue for over a decade (I had a 15 year old computer that still worked - albeit with a replacement motherboard).