If the old turn signals worked, then chances are your wiring and flasher mechanism are probably good. The bulbs these days have a higher resistance than the old bulbs (thinner filaments). The flasher mechanism needs a certain amount of resistance to work correctly, which is why they stop working when a bulb goes out and the resistance goes toward infinity.
If your new signals have a dual element in them it may be possible to wire them both to the turn signal wire. This will increase the load on the flasher, and potentially help. If they are single element signals, about the only thing you could change is the bulb itself.
If you're curious and handy with tools, you could measure the resistance of the two devices, and see if there's a significant difference between them. Also, if the new ones came with a wiring diagram, double check it to make sure you wired it up right. I know, it's insulting for me to say it, but it bit me when I put new ones on my bike, and I had to re-do it twice to get it right. I've been a wiring/electronics/electrical guy for over 30 years. It happens to the best of us.
Hope this helps. Ping me if you need more help.
Luke M
Used to have a 1979 CB750L, sold it as a parts bike, now riding a slightly modified 1984 VT700C. Network/Field Engineer. Central OH, USA, Earth, Sol System, Milky Way Galaxy, Universe.