That's very difficult. People always talk about how underrated the Ninth Doctor is despite there being no negativity towards him that I've ever seen. The Tenth Doctor is very popular amongst fans, casual viewers, and with the BBC themselves seeming to favour him over every other incarnation, it's not hard to say that perhaps the appreciation is a tad overboard. I can barely get through a day where I don't see someone with something nasty to say about the Eleventh Doctor or Matt Smith himself. The Twelfth Doctor seems to be adored in the fanbase, but is frequently abused by news articles. The Thirteenth Doctor gets a lot of love from those who like her, but the hate directed towards her by those who don't is far too excessive. The Timeless Children, despite the only thing we know about them being that they exist, perhaps get more hate than any other Doctor, which seems really unreasonable. The Fugitive Doctor gets a lot of praise from her fans (arguably a bit too much for someone with barely any screen time), but gets such horrific abuse from people who aren't fans of her. So for that, I think I'd have to say the War Doctor because, rightfully so, his appearances on screen were brief and within the presence of other incarnations, meaning most people don't really have a strong opinion of him either way.
