Why is it better? More integration capabilities. You're not limited to the webpage and app, you can use it anywhere you want. Not constantly kicking me out to log in again every few days (their web does this). The ability to select the model and temperature (a measure of how creative the LLM is). Also the default model seems to be much more recent.
And the price. If you use it sparingly you might be paying as little as 20 cents a month instead of 20 dollars. Not exaggerating but it depends on the size of questions and responses. But really to make it cost as much as that 20$ per month with the API you really have to go hell for leather with it.
The cost of the GPT-4 API is ballpark around $0.05 / 1000 tokens. If you want to include a rolling context window, you will easily hit 1000+ tokens if not a huge amount more.
ChatGPT pro gives you 50 GPT-4 queries every three hours. If you're using it all day you might average about 100 daily queries. Using a dedicated GPT4 API would run you approximately five dollars a day for the same thing - that's $150 a month as opposed to flat cost of $20.
How hard is it to hit 100 queries in a day? Pretty damn easy when you realize that most queries aren't usually standalone - instead they involve a back and forth approach which necessitates a rolling context window and you explore the problem space.
When a query (plus back and forth) might cost as much as $0.25, paying for GPT-4 via the API would only net you a whopping 80-100 queries per month before you exceeded the cost of a pro subscription.
The API certainly has its advantages over the web based ChatGPT, but price is definitely not one of them.
I really hate the web interface also. It's constantly kicking me out, so I have to log back in and rewrite my query. And it keeps switching back to GPT-3 which is one of the reasons I ended up using that. Using it with my own tooling is just so much better.
And I don't really use it that much. I just don't have a lot that I need it for yet. I definitely don't even get to the 100 a month :)
Also I don't use it as hard every day. On the weekend I don't tend to even touch it. But you're right, your mileage may vary wildly here.
Good point though I should revisit GPT-4 again. See if it's improved.
I don't even bother using GPT-3.. it's not good enough for my use.