The difference is money availability and the growth rate. Liquid carbon is probably many times less effective than injected CO2 and the plants will grow way slower, so it depends what you have the finances for and how fast you want your plants to grow.
But the most important first is to learn how to grow the plants and have an idea of what to look out for to predict a problem. The fastest the growth, the faster the problems will develop and you'd have to react faster, in case not all goes to plan.
Also, with injected CO2, you'd better start off with a fishless tank until you are sure all is running well with no issues, in case you gas your fish by accident....but that's not necessary if you are careful and know what you are doing.
The easiest is to start with liquid carbon, try growing the plants, see if you can achieve a balance with the ferts and light.
Then you can always start with injected CO2 at any time, increase the ferts, etc... Some folks use both liquid carbon and injected CO2 in heavily planted tanks, because you can only inject so much CO2 before the fish show signs of stress. So they don't cancel each other really.