The answer depends on (A) what you mean by "visitor behaviour" and (B) how much you are prepared to do in terms of adding to or drawing from what's available in Google Analytics 'out of the box'.
GA will track some visitor behaviour 'out of the box'. E.g. the pages the user visits, when they visited those pages, the source/medium of the session, and so on. There are many dimensions and metrics and you can create custom dimensions and metrics.
If you set up ecommerce tracking for GA it will track visitor behaviour related to ecommerce.
If you set up Goals GA will track them. If you set up event tracking for GA it will track events. For example, you might add onclick Events to your buttons or use Google Tag Manager's Scroll Depth tracking trigger. You might want to record form errors as Events so that you can establish where there is 'user friction' in your forms. You could even record if there are multiple correction attempts on an individual field. But again GA doesn't do that out of the box, you must code such that it's recorded in GA as Events.
If you add your Google Adwords acccount details GA will bring in data related to Adwords. If you add your Search Console details GA will bring in Search Console data.
If you set up Google Optimize or similar that records experiment-related behaviour into GA then of course GA can track that too.
If you want to look at an individual user's behaviour you can do that based on the cookie ID (clientId, which can change, so you can't guarantee user A is not user B) or the (custom) User ID, which will work if the user logs in every time they visit. But so far as I'm aware every analytics software has such limitations.
If you want heatmaps, mouse tracking or such, GA doesn't do that. If you want 'engagement value' GA doesn't do that out of the box - you have to decide what that means and how to measure it. You may well want to values to events. E.g. give a value to a call from your website and record the value alongside the call Event. Or you might want to say a form sign-up is worth X and create a form sign-up Event that records that value as the Event Value.
GA doesn't do personalisation - it's analytics software. Google Optimize can do some personalisation.
There are free libraries in several languages that facilitate access to GA's data via the Core Reporting and Multi-Channel Funnel Reporting APIs (examples and also R) and there is lots of sample code on the internet for making use of it. You can also access the APIs via Google Sheets or something like SuperMetrics. Including at user level (client ID or User ID).
For example, I don't use the funnel report in GA, I use Sheets to get data via the API and construct funnel reports per device category, with charts to show trends at each stage too, for the past N days (user choice). I've made a Markov-based attribution model in R that took data from the GA API and attributed value to each page on conversion paths so I could estimate what were the most and least valuable pages.
For free software, this is powerful stuff and there is tons of potential.
Maybe look at the Demo account to get a sense of it? It doesn't have User Explorer or API access but I think the rest of it is there.
I know next-to-nothing about Sitecore and haven't used it on a commercial basis so I can't offer any comparisons.