A website chatbot catches the stranger who found you on Google and has not decided to contact you yet. A WhatsApp chatbot serves the customer who already has your number. They solve different halves of the funnel, and the setup, rules and costs are nothing alike.

In India this question usually arrives backwards. WhatsApp is where your business already talks to customers, so a WhatsApp bot feels like the obvious first move, and the website widget feels like the foreign thing consultants recommend.
The channels are not competing for the same customer. That is the distinction worth getting right before you spend anything.
Who each one actually reaches
A website chatbot talks to someone who does not know you. They searched for "modular kitchen Panchkula", landed on your site, and are three tabs deep in a comparison. They have not saved your number and have no intention of starting a chat with a business they may not use.
A WhatsApp chatbot talks to someone who already took a step. They have your number from a card, a Google Business listing, a click-to-WhatsApp ad, or a previous order. That is a warmer contact and a smaller pool, and the ad spend that fills it is a real cost.
So the honest framing is a funnel rather than a fight. The website catches strangers. WhatsApp serves people who have already raised a hand.
Identity, and what each channel knows about the visitor
WhatsApp hands you a verified phone number before the first word is typed. No form, no lead capture step, no fake numbers. For a business that closes on the phone, that is the single biggest advantage in this comparison.
A website conversation starts anonymous. If the visitor wants an answer and leaves, you have nothing. This is why a website bot has to be built to ask for a number at the right moment, and why what it does when it cannot answer matters more than its answer quality.
There is a mirror-image cost on WhatsApp: the customer now has your number, and the conversation lives in an app that pings a person. Which brings us to the part nobody budgets for.
Setup, rules and who has to staff it
A website widget is a script tag. Paste, save, done, and nobody has to approve anything.
WhatsApp is a platform with a gatekeeper. You need a Business Manager account, business verification, a phone number dedicated to the platform, and in practice a solution provider to route messages. Business-initiated messages have to use templates that Meta approves in advance, and there is a customer service window after a customer messages you within which you can reply freely; outside it, you are back to templates.
Those rules exist for good reason and they shape what you can automate. A follow-up two days later is not a free message you send whenever you like.
Then there is the staffing. A WhatsApp message carries the expectation of a person. Read receipts make silence visible in a way a website chat does not, and an unanswered WhatsApp at 9pm reads as being ignored. A website bot that says "I'll have someone call you tomorrow" is accepted. The same sentence on WhatsApp, from a number that was replying instantly a minute ago, is not.
What each one costs
The website widget's cost is the vendor's fee. Flat plans exist, and the cost drivers are the same ones any AI chatbot carries.
WhatsApp adds a platform layer. Meta bills for conversations through the WhatsApp Business Platform, with rates that vary by category and country, and the rules have changed more than once. Your solution provider usually adds a markup, and some bundle a monthly fee on top. Check Meta's current published pricing rather than trusting a figure in any article, including this one.
The practical effect is that WhatsApp costs scale with volume in a way a flat website plan does not, and a campaign that works well produces a bill that reflects it.
What is identical on both
The bot is only as good as what it can answer from. Both channels need published prices, real policies, actual timings and the twenty answers your staff give on the phone. Both fail the same way when that material is missing, and both do damage when they guess instead of refusing.
Neither one fixes a website that does not say what things cost. If you are choosing between channels while your pricing page says "contact us for a quote", you are solving the wrong problem first.
A sensible order for a small business
Start with the website widget if your customers find you through search and you are losing enquiries outside business hours. It is cheap, the install is minutes, and a month of conversations tells you what your customers actually ask, which is the input everything else needs. Chatterbox is website-only today, which is a limit worth stating plainly rather than a strategy.
Add WhatsApp when you have people to staff it and a reason for customers to message you first. Post-sale support, order updates and reorders are where it earns its keep, and click-to-WhatsApp advertising is a real acquisition channel if you are already buying ads.
Run both when the website catches the stranger, takes their number, and the conversation continues on WhatsApp where your team already works. That is the arrangement most Indian small businesses end up with, and it works better in that order than the other way round.
The next step is smaller than picking a channel: read your last fifty customer messages, sort them into "asked before buying" and "asked after buying", and let the split tell you which channel to automate first.