Does it matter to you who you sell your house to?

Question for everyone selling their homes - I have absolutely fallen in love with a house that is quite a bit out of our budget. We’ve offered £15,000 under the asking price and didn’t get an immediate no. The sellers seemed interested in who is buying their house and I’ve written a letter to them explaining that this would be the family starter home with my partner and how much we want to pay down roots in that particular area. We are also cash buyers and not currently mortgageable (I’m a mature student and my partner hasn’t got full residency yet) so I feel like it helps that we have the cash but constrained that we can’t add more through mortgaging. The EA has told me there is another offer in from an investor who wants to use it as a buy-to-let that is closer to asking price. The fact the vendors haven’t immediately gone with that gives me hope but we just can’t stretch to where the investor is. So I’m wondering - would it matter to you what someone wanted to do to your house ie living in it and starting a family or would you go for the higher offer?