4 or 5 years ago, Mr. Athena had a Sony Vaio laptop. It’s long since died, but we still have the AC adaptor. I just found it in a drawer.
I just bought a new Vaio. The AC Adaptors aren’t the same size or shape, but they do have the same connectors on them, and all the writing on the back says the same thing:
Sony AC Adaptor
19.5V
Input: 100-240V
50/60Hz 125-160VA
Output: 19.5 V 3.3A
Can I use the old one with my new Vaio?
The only other thing to check is the polarity. I looked around on Google Image search and found this image:
http://www.nbook.ru/at/sony_vaio_pcg-grx570/power.jpg
If you tilt your head, just to the right of the large ‘19.5V’ is a little drawing of the plug with positive and negative indicators. These must match on both of the adapters. This is even more important than an exact voltage and/or current match. If one or both of the adapters lacks the drawing, anyone with a voltmeter should be able to help you out.
The polarity matches; so far so good!
Anything else I should consider?
From past experience in owning four Vaio’s, if the plug fits, the powers the same. Of course in comparing the info printed on each adaptor I felt safe in doing so. 
Check for pods in the basement. Sony used the same sort of power adapter (even if it looks different) and same plug for two different products five years apart? Very unusual for them!
As long as the plug polarity is the same, the voltage is the same and the plug is the same, the only other thing to watch for is current. As long as the old one from the drawer isn’t rated for 0.5 A and the new one is 4.0 A, you should be just fine as long as the ratings are fairly close.
As an example, I’ve had no problems using old adapters on new IBM/Lenovo ThinkPads. The old ones are rated to put out 3.5A and the new ones put out 4.5A, but I haven’t had a problem.