As you can see in the graph above, Tinder is more popular in the US than Badoo, however the opposite is true in many other countries.
We will see what advantages and disadvantages this situation has.
First Steps
Badoo's sign-up process is automatic once you link it with Facebook. Something similar happens with Tinder; you only log in with Facebook, pick the photos you want to show, and establish some preferences like sexual orientation, and that's it.
As you can see, no differences here.
Badoo verification process

Badoo has a simple verification system. They show you a photo, and you need to copy the pose using your phone's camera. You can see who is a verified user and who is not, This is great because it prevents Catfishing and bots.
Social network integration
In this aspect, they are both doing fine. On Tinder, you can link your Instagram account, show your Spotify playlists, and sign up using Facebook. Badoo is pretty much the same in this aspect, but it doesn't allow Spotify integration.
Photos & profile
The only difference is that you can also upload videos in Badoo.
We have a series of experiments with Tinder profiles to know which ones perform better. You should check it out.
Example of the kind of analysis we've done:
Demographics
It's almost impossible to know their demographics. If you look at the opening graph of this article, you'll notice that Badoo is popular in different markets.
Their worldwide break-down by SimilarWeb looks like this:

The age and gender distribution may be different in your target area though, the only way to know is by trial and error. It's important to underline this point, you won't know without trial and error, no matter what people says in the Internet.
User Approaches
Tinder is mostly only for dating, and it's perceived as such pretty much everywhere. Badoo has a more lax approach. There's a more friendly vibe perception in some countries about Badoo, that allows girls to downplay the possible slut shaming by their peers, thus allowing a more female leaning-demographic in some areas.
Badoo allows, in fact, to filter by intentions, such as just hookup, a short-term relationship, a long term relationship, marriage, etc.
Typically, users that use non-mainstream apps, in particular girls, are more easy to connect and chat with, because there isn't the ever present avalanche of interactions in the most popular apps. That means that if you're in a Tinder-dominant area, you may have better results with Badoo, and vice versa. It's not always the case, but it's worth trying.
Matchmaking
Badoo and Tinder have similar matchmaking systems. You like a person, that person likes you, and you two get a match. It's possible to search by location in both of them (but it's free in Badoo, while it's a paid function in Tinder), and establish distance as a filter if you do not want to travel somewhere else for a date.
It is possible to talk with people without matching in Badoo, but only if the target profile is not popular. Badoo restricts the ammount of messages a given person can receive, mostly aiming at solving the avalanche problem we already mentioned. The only way to overcome this limit is by either matching with that person, or paying.
Users location
If you look at the opening graph, more than 60% (30 Million) of Tinder's users live in the US. Badoo has users in more than 200 countries and territories, with 46 different available languages. Brazil has the largest number of users with 11% (55 Million).
Pros and cons
They are strong in different countries. Badoo allows to look for people in other locations without restrictions, you don't need to trick your GPS or pay to list people from elsewhere. Also, they don't seem to have anything similar like the ELO Tinder algorithm, as far as we know. The only downside may be related to the particular demographics of your location.
Paying features are also nicer than Tinder. There's a Badoo Premium feature, simar to the Tinder's one, but there's also a credit system that allows you to pay for specific features without forcing your into recurring payments.
So, in summary, Badoo is like Tinder but with extended features. In my opinion, the only upside about Tinder is that it's more popular than Badoo in some places.