Shrewsbury are one of the two sides currently in the league who are unbeaten in league matches against United - the other is Stevenage. Both teams have of course lost to us in other competitive games.
I can't speak for the away matches but United were terrible in the home games in 1985 and 1988 (Bassett's first home game, I think) and poor in 1987, when they were bailed out by an equaliser from a corner from Big Stan. Marginally better in 1986 - again, the first home game - but Morris missed a penalty.
I saw all 5 games with Shrewsbury at home in the 80's when I was a teenager (what a youth I had)..
25/10/83: D2-2 in the League Cup. Edwards put us one up with a goal where he blatantly handled it before scoring (still to be seen on youtube). The Shrews then went 2-1 up before Arnott equalised for us. However, it wasn't good enough as Shrewsbury had won the first leg 2-1 and we went out 4-3 on agg. Interestingly, Steve Ogrizovic was in goal for the Shrews having been recently released as Liverpool's resreve goalie and before resurrecting his career at Coventry.
27/4/85: L0-1, this was part of a run of 9 games at the end of the season where we failed to win one and we were only saved from relegation as our 3 main rivals (Notts Co, Cardiff and Wolves) managed to do worse. This game was notable for the return of our potent strike force of Edwards and Eves after some time out through injury. However, they did nowt in a game made memorable only by a late April snow storm.
31/8/85: D1-1. This was the game in which Peter Withe got his first goal, equalising an early Shrews goal. In the second half, Morris had the chance to win it with a pen but it was saved. It was the 2nd home game - the 4-0 win over Basset's Wimbldeon the week before being the first.
23/8/86: D1-1. First game of the season and much doom and gloom around with Edwards being sold to Leeds a couple of weeks before. Another boring game where Stan put us 1-0 up early in the 2nd half and Shrewsbury equalised with about 15 mins left.
13/2/88 L0-1. Bassett's first home game and a woeful performance. Bassett publicly said that it was not good enough after the game.