I use all three programs.
Python can do everything that R can do and R can do everything that Python does, but I must say R is superior to Python when it comes to the packages. For that reason for most econometric analysis I usually default to R. I find also producing nice standard statistics graphics with R easier (but for maps I prefer Python).
However, Python is far superior for web-scraping, numerical analysis and sentiment text analysis (although R has some good packages for that as well). Also, I prefer to use Python when I need to set up my own program as programming in Python is more natural (if that makes any sense) than in R, unless the program can be build easily from ready made functions from various packages.
I always recommend to people around me to learn both Python and R - the difference between them is not that big and with R you don’t really need to invest heavily into programming skills but just basics and then use packages.
Also, Jupyter Notebooks that can accommodate both R and Python make using both of them easier.
When it comes to Stata I use it only for a educational purposes (I teach econometric tutorials at university). To be honest I don’t like stata for several reasons:
Stata is not a freeware and i don’t think that the price tag is justified given that it’s inferior product compared to free ware programs like R and Python. If you can get it for free from uni then you probably don’t care about that but still it’s something to keep in mind.
Stata is a program not a language so if you want to create a new complex function you need to separately get and learn Mata (statas programming language).
Stata has some serious limitations on matrix sixes even in the most expensive edition the max mat size is 11000 which is serious limit when you work with panel data and have to run some iterative model with large number of variables. You will be routinely forced to run for example panel LR heteroskedasticity test on random subsamples even with the most expensive edition.
Creating beautiful graphics in Stata is nearly impossible - now don’t get me wrong you can make some decent graphics in Stata but it pales in contrast to what you can do with Python or R.
Stata is clunky with time series analysis. If you look for easy to use program for time series analysis it would be EViews. For example Stata can’t handle if you have quarters that are expressed in date format it will think you have gaps in your time series and won’t let you run basic time series commands until you create new time series variable. Also the offer of time series models is quite low and programming your own is painful.
While technically possible webscraping or numerical analysis in Stata is hell - if you need that for your work don’t use it.
However, Stata has also few advantages:
It’s more user friendly than R or Python, and can be even used without coding through interface (that’s why we use it for tutorials for students as a first program they see so they don’t get overwhelmed).
Doing some adjustments to datasets creating dummy variables etc is easier compared to Python or R but that’s mostly because in both Python and R you can have various types of data, lists, data frames etc.
With purchase to Stata you get access to Stata forums - it’s something like stack exchange but they actually pay professionals to give you answers there and often beside support you can get there very good advice even on econometrics, and you will usually get advice really quick.
I personally would not use Stata for my own scientific work. Python and R are superior to every aspect of Stata - but it’s very good starting program for students.