I always cringe a bit when I hear a freelancer ask a perspective client "What's your budget?" Isn't that the same as asking "How much can I get away with charging you?" Or "Can I charge you more than I normally would without you realizing it?" For me, there is absolutely no reason I need to know the client's budget. I need to know the breadth, scope, and complexity of the project, that's all. It's for me to determine if it's a $500 or $50,000 job, then they can determine if they wish to pay for it.
I rarely get a budget from any any client (but I don't use online services either). If I do get a budget it is after my quote in an effort to possibly lower my costs to meet a lower budget (or as a negotiating tactic on their end).
I price all work according to what I need to earn. Isn't that how everyone should be pricing? I've calculated my hourly rate, then bear in mind current market rate trends, and ensure I'm never at a loss for any project. Is there a possibility that I could charge another 20% and retain the work, maybe. But is it worth finding out? Most often not. As long as I'm earning what I've determined I want to earn why chase after unicorns and rainbows? You know, a bird in the hand is worth two in the bush and all that.
If I calculate, based on the project scope, I need to charge $5000 to complete it. Then that's what I need to earn and that's what I quote. It makes no difference if the client has an $8000 budget. I price based on my rates, not what the client has in their pockets.
Imagine this... you go into a store and want to buy a stick of gum. You walk up to the cashier and she looks at you, and then says "Well, we would have priced that gum at $1, but since you have $20 in your pocket, how about we charge you $19.99 for it?" -- This is what you are trying to do by pricing based on the client budget. It's ethically questionable and ultimately will do you more harm with clients than good.
Determine your rates and then calculate project costs based on that. The client's budget should make no difference to you at all. Unless they express their budget is lower than your quote/bid and then it's up to you to determine if you wish to lower your pricing to meet a lower budget.