I love both- and I love the fusion of the two that occurs with use of the Etteilla tarot decks. If you haven't checked them out, you should!
In general- I find that cartomancy is great when I need details, and with questions surrounding family, work, home, love, etc. If I need timing or details, my lenormand comes out.
Tarot, to me, works on a more esoteric level. So the details are not there, but it gives a richness to the patterns behind your thinking/actions. And it is great for more spiritual questions.
The Etteilla deck does both. There are grand tableau spreads you use with the Etteilla tarot, card meanings are changed by surrounding cards, meanings are very similar to the cartomantic meanings- but you have associated majors as well- to add in the spiritual, the alchemical esoteric nuance that is missing from cartomancy decks. I love it- there are a few different "types", but my heart is held by the Grand Etteilla. It is a process to learn how to use it though- so that can be very off-putting. I love it- must have the same wacky though processes as M Alliette.
I first learned to read with an old euchre deck (along with using a pendulum, reading tea leaves, geomancy and aeromancy- thanks to my eastern European grandparents). I also use runes- which takes things to a whole different level. It never fails to amaze me how different each type of divination feels, how it works, how it expresses itself. Tarot came later- but after practice, I familiarized myself with it so that now I am as comfortable with a tarot deck as I am with a deck of cards. My recommendation would be to work with both! Each has its strengths and weaknesses, which is why it is so amazing to learn more than one method- so that you can use the one that most works with the situation at hand.
Great question!
Just figured I would add in my 2 cents!