I've had a chance to run these side by side and the clear winner (IMO) is TRIGGERcmd.
My HA-Bridge stopped being able to have Alexa recognized new devices
this is what got me looking into TRIGGERcmd)
HA-Bridge still gives me control over my x10 devices I had previously discovered so I compared controlling those x10 devices.
Occasionaly I get the "device is not responding" reply from Alexa for devices configured with HA-Bridge.
HA-Bridge has a helper for Home Genie and other software which works great.
If you can get Alexa to see new devices created it would be possible to trigger the same things.
Sadly HA-Bridge stopped being able to work with Google some time ago.
The Bridge mimics a Philips HUE hub so code must be continually kept updated as Amazon changes things.
With TRIGGERcmd I've yet to get this "device is not responding" reply and maybe it is my imagination but devices seem to respond quicker.
Unlike HA-Bridge there are not helper files so setup is similar before helper files were added to the Bridge. Maybe not quit as difficult.
TRIGGERcmd requires a yearly subscription to be able to run from multiple computers and issue a Voice command more then once per minute luckily I don't require this. ( I do have ways around the 1 per min call if required)
TRIGGER does both Alexa and Google Home though I prefer Alexa. I've tested with both.
TRIGGER uses skills which once created, Amazon and Google maintain so they always work with the intended service.
TRIGGER does have a Github page but also has a forum which if a question is posted it usually gets a quick reply.
I've only been using TRIGGERcmd for slightly over a month verses years compared to HA-Bridge, so issues may pop up.
I removed HA-Bridge from my PiX10Hub a day or so ago (hope I don't regret it).
My off grid place still only uses HA-Bridge but I suspect I'll be moving to TRIGGERcmd once I need to add a new device for Alexa control. Or maybe the "device isn't responding" reply may get to be too much.
If your using either or both of these I'd love to read your impressions.