Appointy is good for small businesses looking to outsource some admin work and get appointment bookings done online, especially if you don't have a huge client base. You can input the individual client's name in the system so it helps to personalize your services. It's not so suitable for larger companies. It's a good price for small businesses. Sometimes the design can be a bit clunky and the user interface isn't perfect, but for the price and google integration it's well worth it.
Doodle is great when you need to coordinate dates among a group and don't want to send a bunch of group emails or texts. It allows a number of dates to be proposed and the group can easily see those dates that are most preferred. If you need to do something more complex than that it may not be your tool.
Doodle approaches this problem different than most other scheduling platforms I've looked at (and I've looked at most of them). Doodle allows the person who is making their calendar available for scheduling to make the final decision on the meeting in contrast to other platforms that typically do it the other way around. Both can be beneficial depending on preference
I love that Doodle allows for proposing multiple times, which is a feature I've yet to find on other scheduling platforms (and I've looked at/tried a lot of them)
Doodle makes the scheduling process very simple even for someone who's never used it before
Doodle has customer service support available as needed, but honestly, it is so easy to use that I have rarely had to seek support. They are always a click away and responsive to resolving any need or to clarify the next best step to using Doodle to meet my needs.
We didn't evaluate any other products as we weren't actively looking for such a product. This is a product that is not directly part of our core business but proved to be a good match with an issue that we unknowingly had. Only after an enthusiast colleague showed the demo did we find out that there was an issue that many colleagues experienced.
Doodle is more customizable and I love the animation aspect. It is missing the engagement piece, but again I am new to it so there may be features in Doodle that I haven't discovered yet.