United are without a win in four matches and are winless in 10 games at their Tannadice home, but have won four of their nine away matches this term.
Brown's Dons, meanwhile, have three home wins from 10 attempts.
"Dundee United I always think are a smashing team, a good football team," Brown, who watched United lose 4-3 to St Mirren on Sunday, told RedTV.
"They're very dangerous. It's a very difficult game, even more difficult because they play better away and so do we, unfortunately.
"Before the (St Mirren) game they were bemoaning the fact that they hadn't won in nine home games.
"That makes 10 home games, which means they must be getting an awful lot of points away from home, because they've got 25 points.
"They're dangerous opponents and very good from middle to front but they're a bit vulnerable at the back and maybe a bit more so because (Brian) McLean was sent off."
Brown admires United strike duo Johnny Russell and Jon Daly in particular, but the visitors may shift striker Daly to defence with McLean suspended.
That could play to the Dons' advantage as they seek to win ahead of the winter break, which Brown believes is coming at the right time for his stretched squad.
He added: "Hopefully we can get something successfully negotiated against Dundee United and then the break will be fantastic for us.
"If ever a team needed a break to get players fit, it's Aberdeen.
"Hopefully we can get a good result on Wednesday and then pick up from there with everyone back fit again for a week's hard training before we play Inverness."
Captain Russell Anderson is in line for his 350th appearance for Aberdeen on Wednesday.
Brown added: "That is fantastic. No-one deserves more credit than Russell in every respect. He represents Aberdeen brilliantly."